Basics of MTTs SnGs and Cash Games
An MTT is a Multi-Table Tournament where there is no limit (or an extremely high limit) to the number of players in the tournament. The tournament continues until there is only 1 player remaining. Once you enter the tournament, you cannot quit until you lose all your chips or win money. Typically, about 10% of the players get paid winnings with the top positions getting paid much, much more than the rest of the paid places. So if there's 1000 people in the MTT you want to finish in the top 100 to make a "min-cash" and hopefully in the top 9 (the final table) to rake in the big bucks.
An SnG is a Sit-n-Go where there is a specific limit of how many people can play (such as a 9-player SnG). The tournament will not start until there is that many players, and there can be no more than that many players. Once again, you cannot leave a Sit-n-Go until you either lose all your chips or win money. In a Sit-n-Go, a higher % of the field gets paid. For instance, in a 9 player SnG they typically pay the top 3 places (or top 33%).
A Cash Game (aka Ring Game) is made up of a single table of players. You put cash on the table and directly play for cash. Each hand you win or lose is actual cash you are winning or losing. In a cash game you can get up and leave at any point, so if you win some money you can just get up and keep it, or if you lose some money and don't want to lose more you can get up and keep whatever is left over.
In MTTs and SnGs the blinds constantly increase in size.
In Cash Games the blinds are always at the same level and online you get to pick what level you want to play at.
Playing a TAG (Tight AGgressive) strategy is highly recommended in all styles. You should do research on that specific strategy. However, there are some differences between the types of games.
With Cash Games, the blinds never go up so you can spend more time sitting around waiting for a great hand.
With a SnG, the blinds go up periodically, so you need to play some more
hands (not bad hands, just more hands) in order to keep a good stack size (20+ BBs). However, in SnGs you're mostly just trying to outlast your opponents because there are so few of them.
With an MTT, You cannot just sit around waiting to outlast your opponents. The blinds get way too high for that. You have to open up your range and play simply good hands and even some mediocre hands thrown in to try to win chips. In MTTs it is ultimately important that you maintain a healthy stack size (20+ BBs) and if all you do is sit around waiting for a great hand, the blinds are going to go up on you and take you out fo the tournament before you reach the money.