Both are.
Tactical shots are quite a bit easier when you know one exists, however training the themes of tactics continually forces you to unconsciously notice such things and make spotting such situations possible.
The trick is the use the knowledge gained about the themes listed above during a game to force winning positions.
I have actually increased my knowledge of chess alot due to puzzles because it taught my mind to start thinking that way.
From what I've heard, studying tactics and annotated master games is the way to game.
BTW: most good tactics books group puzzles based on themes so you can see reoccurring themes in your tactics study.
I agree with Enimar. I think it's important when doing tactics puzzles to actually be able to explain the logic behind what makes the tactic possible. I used to solve puzzles without always consciously knowing why a tactic "worked", but for me, being able to explain the rationale behind a tactic sharpens my vision at the board and also helps me see further ahead to where the position might go.
spoiler> On the other hand some say, working on tactics can be overrated,
Who are these some, and do they know how to play chess? 
Teichmann, Fine, Karpov, Polgar--they all say chess is 95%+ tactics. I see players argue about the best methods for learning tactics, and when to look for tactics, but I've never heard anywone argue that working on them is not very important for a USCF 1300- or 1400-rated player to improve.
spoiler> when you are actually playing, you are never helped or told of that tactical opportunity, thus you may miss it.
I check for possible tactics every move.
Agreed, you need a mix of both. The puzzles help your observance skills and finding ways to win or gain the advantage. Learning the tactics behind the success leads you to apply it in other similar situations than just in the puzzle.
Or you could kill two birds with one stone and get 600 Practical Chess Exercises by Cheng and practice tactics in real-game situations! AHA 
(Good book by the way, pretty hard though I'm gonna need to go through it several times).
On a somewhat side note, a tactical shot was the only way for me to save a game where I walked into an ugly pin. Instead it allowed me to go up a full rook and convert the point. I'd have never seen it without constant tactical training through Chess Mentor, though this isn't the place for discussion of that aspect on chess.com.
From what I've heard, studying tactics and annotated master games is the way to game.
BTW: most good tactics books group puzzles based on themes so you can see reoccurring themes in your tactics study.
This: and I would say that when you have studied enough puzzles your tactical vision increases dramatically and its almost as though a whole new world of chess opens before you. You WILL see tactics in your game, a heap of them that you need to defend against and use against your opponent to either gain material or a positional edge.
I agree with Teichmann, Fine, Karpov, Polgar and 'likesforests'; chess is 95% tactics, perhaps even 99% tactics. Personally, I never really got into solving puzzles for tactical training. I'd much rather train my eye by playing gambit systems in blitz games. This works fine for me, but to each his own. I think I like to 'feel the flow' of the games, as opposed to trying to solve static puzzles. I guess that's why I have so much time left on my free Tactical Trainer...lol
How do GMs practice before major tournaments? How did the GMs of old practice before major tournaments? What did most GMs play early in their careers? Contrary to popular belief, the answer to these questions is gambit systems. All GMs include a few gambit systems in their practice and opening repertoires, because playing gambit systems force players to think tactically from the start of the game.
I believe that it's important to learn how to form your own 'tactical shots' by following opening guidelines and being aggressive. Tactical opportunities arise from well-placed pieces. Therefore, I believe that when trying to learn tactics, playing trumps puzzles.
PS. The tactical trainer and Chess Mentor on Chess.com are excellent. Furthermore, IM Jeremy Silman is one of the most respected instructors out there.
spoiler> On the other hand some say, working on tactics can be overrated,
Who are these some, and do they know how to play chess?
Teichmann, Fine, Karpov, Polgar--they all say chess is 95%+ tactics. I see players argue about the best methods for learning tactics, and when to look for tactics, but I've never heard anywone argue that working on them is not very important for a USCF 1300- or 1400-rated player to improve.
spoiler> when you are actually playing, you are never helped or told of that tactical opportunity, thus you may miss it.
I check for possible tactics every move.
Silman rails a bit on Maza and his tight focus on tactics training.
http://www.jeremysilman.com/book_reviews_js/js_rapid_chess_improv.htm
In my 3rd edition of How to Reassess... , the character in the beginning of the book stalls out below master because his foundation was incomplete. I think Silman was referring to Maza.
I get that, but from my perspective lots of tactics are in order, and at my age I find myself more than 200 pts below expert and would love to stall a class higher. That's about as good as I could hope for, and that might require lessons from a master.
Silman, of course, has a more positional style than some masters. But even in HTRYCv3 he discusses combinations and tactics before imbalances:
"Since the position screams for 1.Qxa6 to be played, White has only to calculate the consequences of a Black checking onslaught to see if it is a correct decision tactically. As it turns out, Black gets some macho checks and then has to resign: 1.Qxa6 Qh1+ 2.Kf2 Qxg2+ 3.Kxe3 Bg5+ 4.Kd3, 1-0."
"To do this we will borrow Kotov's suggestion that candidate moves be used. A candidate move is all the possible (meaning reasonable) replies your opponent might make (or if it was your move--all the moves that lead to the fulfillment of your plan). Kotov recommends that you mentally list these possibilities, so on paper the choices would be like this: A) c4; B) Qe4; C) Nc3; D) Nb4; E) Bb7; F) Qxc5; G) Nxe7+. Note that all of these moves either defend the hanging knight or try to take advantage of the fact that Black's Queen is sitting on the same line as White's rook on d1."
I know a puzzle book I solved the day before my tournament this Sunday helped me find a winning shot, and one of my opponent's credited the chess.com tactic trainer for helping him find a winning shot. Solving puzzles works for many players, like the Polgar sisters, although of course it's not the only way to study tactics. :)
Tactics are the integral part of the game. Everything you do on the board is centered around tactics. You should practice them as often as you can. Even positional greats like Tigran Petrosian knew of the importance of tactics in chess. Without them, you wouldn't even have the game.
Once you know tactics like the back of your hand, you will know a lot about how chess works.Positional and strategic play must be grounded on sound tactics anyway, so you have to learn them no matter how you look at it.
I personally have never made a list of candidate moves in my mind before looking for my opponents responses. I do try to calculate all the reasonable and usually forcing, responses he/she can make before I move though. I more just find these on the board as I go along and determine whether or not they would work, instead of looking for all possible replies, listing them in order, and trying to go through all of them.
Tactics are the integral part of the game. Everything you do on the board is centered around tactics. You should practice them as often as you can. Even positional greats like Tigran Petrosian knew of the importance of tactics in chess. Without them, you wouldn't even have the game.
Once you know tactics like the back of your hand, you will know a lot about how chess works.Positional and strategic play must be grounded on sound tactics anyway, so you have to learn them no matter how you look at it.
I figured it's the other way around, without sound positional play tactics don't really exist...
What about Michael da la Maza's ( author of: rapid chess improvement) idea of doing 1000 tactics a day, isn't it a little extreme. How much is too much? How much is enough? Yes I read tactics are 95+% chess but if that's the case , the rest5% is opening/endgame theory? How about game analysis?
What about those award winning mate in 2's? Are they a help to become a real good chess player?
spoiler> What about Michael da la Maza's ( author of: rapid chess improvement) idea of doing 1000 tactics a day, isn't it a little extreme
It would be, if that were the daily routine he encouraged, but of course it's not. If you want to understand what he really recommends, a method focused on pattern recognition, calculation, and thought process that harnesses the proven benefits of spaced repetition, then explore this page and the links at the bottom. You'll also find info there on some of the players it's helped. It's not the only way. To each their own. :)
spoiler> What about Michael da la Maza's ( author of: rapid chess improvement) idea of doing 1000 tactics a day, isn't it a little extreme
It would be, if that were the daily routine he encouraged, but of course it's not. If you want to understand what he really recommends, a method focused on pattern recognition, calculation, and thought process that harnesses the proven benefits of spaced repetition, then explore this page and the links at the bottom. You'll also find info there on some of the players it's helped. It's not the only way. To each their own. :)
Thank you, by the way where is he now?
spoiler> Thank you, by the way where is he now?
I have no idea what he did after quickly achieving expert as an adult and publishing his training method--certainly nothing of interest to chessplayers.
Many believe that if you do 10-15 tactical puzzles a day (or even more), you may become a stronger chess player. On the other hand some say, working on tactics can be overrated, since you KNOW that there is a tactical shot and you are likely to find the solution soon. The problem comes, when you are actually playing, you are never helped or told of that tactical opportunity, thus you may miss it. So they figure it's best to be aware of tactical THEMES that the current chessboard presents, and find tactical shots that way, and not do tactic puzzles all that much. (Unless you love doing them regardless)
Which school is right?
PS: Tactical themes can be: back rank situation, undefended piece, pieces on same diagonal/file/column/rank, lack of king safety, pieces situated that they can be forked by a knight....etc...