Well, a ten minute game means that you have ten minutes for YOU to move.
For a 15|10 game, initially you will have fifteen minutes and you will get an extra 10 seconds when you move.
These are live chess.
For online chess, it is a turn-based game.You can have as less as one day to as much as 10 days to make your move.
Since you are a beginner here,I would advise you to play a 30 min game first
I am new to online chess and i dont know what the game types are exactly like 10min or 15|10.