How does the strategy that we play at a tournament differs from the strategy at a table? What should we do differently?
There is one big difference between cash games and tournaments:
In a tournament, a player's goal is to "cash" (reach a paid placement). On the other hand, a player in a cash game is strictly required to accumulate chips in order to win.
This means that to find success in tournaments, it is not necessarily required that a player win pots, although it would be beneficial if they did. As long as a player has a decent sized stack, a tight fold could have more value than putting chips into the pot.
Therefore, a fold in a tournament has value, while a fold in a cash game has no value. This is the key difference between tournaments and cash games.
In terms of strategies, I would suggest to have these goals in mind for every hand. It is a bit too general of a question for me to give specific strategies because a lot of situations can arise in different formats.
This is a very broad question and depends a lot on your own personal play style at a cash game to compare it to how you would play in a tournament so this is both an extremely broad and an extremely subjective question.
The first thing you need to realize is that your chip stack is constantly reducing in value in an MTT because the blinds are increasing. The only way to win a tournament is to win chips and you are racing the clock.
In a cash game, however, you can (generally) afford to take your time and make safer decisions, wait for spots or play tight if that is your cash game style.
There is also a significant difference in tournament versus cash Bankroll Management (BRM). I could provide links to get you started on each but that would be nothing more than a quick Google search could find you.
If you are really stuck and at least somewhat serious about poker start by reading some books! There is a great list: Here that I frequently point people toward and am working through myself.
I have tried to provide a broad and general answer to suit the question. pretty much every statement I have made has edge cases and exceptions so keep this in mind
For survival you need to play more exploitative in MTTs. In your average cash game, Playing more towards GTO (Game Theory Optimal) is usually profitable. your goal in a cash game is to profit, your goal in a tournament is to collect chips at a certain minimum rate to avoid being short stacked and remain in contention for cashing or even winning the tournament!