Score in Chess.com

As far as I know there are two different scores in Chess.com online depending on the timing of the game, so if you play a game of 10 min or less you will score in Blitz ranking, and if it is between 15 and 60 you will score in the fast ranking. This statement leads me to the further questions: 

- Is that how it works? I did not find any clear explanation of that

- What score really counts? So at the end, which is my score in Chess?

- What ranking is scored when playing 5/5 or 10/10 or similar? 

I always played 5 min and 10 min, and every game I scored +8 or -8, sometimes +9 or -9, or +7 or -7, but then I played today a 10/15, which I understand I was scoring in the fast ranking, and after winning I got +135 points? How does that work?

There is no main "score" or rating that really counts. For decades, over the board ratings in slow chess were the only ones that existed but now there are many ratings from different sites, mostly based on faster play.

They are not directly comparable to over the board ratings.

For standard chess. there are currently 3 live chess ratings (bullet (<3 minutes), blitz(3 up to 10) and rapid (over 10)) and a daily chess rating for 24 hours plus per move chess.

Recently, the ability to play variants like Chess960 and Bughouse and other variants has been added to Chess.com too. They are rated too.

How ratings work here have been explained in many previous posts. Here is a good one, written by the guy who runs Chess.com:

https://www.chess.com/article/view/chess-ratings---how-they-work

 Okay, thank you.

Then, as my last question: Which Chess timings (in standard Chess) apply to each ranking?

For standard chess. there are currently 3 live chess ratings:

• bullet (<3 minutes),
• blitz(3 up to 10) and
• rapid (over 10)

Can someone explain why I only get 4 points for checkmate rather than the usual 9 or 10 points for checkmate?

Depends on the rating of the player you beat. The better the player, the more rating points gained.

thanks