What people actually do, and what makes sense, might not be quite the same. The main difference between tournaments and cash games is the fact, that in tournaments you are not rewarded for winning chips but for outlastning other players. This mean, that the value of chips is not constant, which is usually referred to as ICM. In an MTT the winner might take down 20% of the price pool, so at that point each chip is only worth 20%, what it was at the beginning of the tournament.
ICM mean, that you should generally be more conservative in a tournament, especially when risking a large percentage of your stack. It is especially bad to get involved in a huge pot against the table chip leader, if you already have a significant above average stack. So pot controlling in marginal spots and getting to cheap showdowns is part of tournament strategy.
The other difference is, that blinds go up in tournaments, which mean, that after a while stack sizes will get shorter, than they are in a cash game. So as a tournament player you need to learn to play with many different stack sizes, and part of this is the push-fold game, when stacks get very short.
Push-fold is also the only situation, where you might want to play more aggressive in tournaments. This is because, ICM mean, that your opponent need more than 50% equity to profitably call a jam for his entire stack or most of his stack. So against players, who are aware of this, or who just want to get in the money near the bubble, going all in gives you a lot of fold equity. Usually tournaments also have antes, which makes taking a pot home uncontested preflop more valuable. Blind stealing is therefore more important in tournaments, especially as stacks get shorter.