Tournaments and cash games are quite different, true. But I don't think anybody discussed something I think is important -
I'll do so with an example hand, and we'll use variables for BBs.
Let's say we're in the BB, and it's checked around to us, in a four-way pot. We have suited connectors, but not big enough for us to raise out of position, we'll go with 8s7s. We decide to check. Remaining players are SB, Hero (BB), MP, and BTN.
The flop hits us big, with 5s6dKs. We've flopped an open ended combo draw. Here are some of the differences in how we might play it.
We flopped a hand with a lot of equity, assuming nobody shares our hole cards, our straight outs, or is on a better flush draw, we have a whopping 15 outs to beat even a flopped monster, which gives us something like a 63% chance to improve to a straight or a flush, and a very small (almost negligible) percentage to improve to two pair or a flush to beat the likes of AK.
In a cash game, we have a few options how to play this, in a limped pot too much aggression isn't going to get paid off, unless somebody played Kx and hit two pair, slowplayed a monster (KK, AA), flopped two pair w/ 65, or a lesser draw, like 34 for instance. We can choose to play the pot slowly and hope to improve and get paid, or play it aggressive and hope somebody gives you some action and you improve, or play it aggressive and hope everybody folds around. From short-stack, you might check w/ the intent to check/raise jam, while you're still looking to your chips in there with a lot of outs. From a middle stack your play might be trickier, you will have a couple actions, and from deep stack you'll have all the options listed and a few more.
I recently had a flop like this in a cash game sitting around 400 BBs effective stacks in a 3-way pot. With a pot of around 20 BBs, I bet out about 15 BBs, villain A raised to 30 BBs, Villain B reraised to 60 BBs, I called, Villain A reraised to 120 BBs, Villain B called, and I jammed for the remainder of my 400 BB stack. Villain A folded, and villain B, after much contemplation, folded. They ran the cards to the turn and river and I was unimproved, but I took down 240 BBs on the flop with a monster combo draw. Also - both of my villains were terrible.
That's just one example of cash game play.
Now, assuming same pot-size, 20 BBs, and I'm at 50 BBs left, there is a lot more reason for me to open-jam that pot, then check/raise, because when my open-jam induces a fold from weak Ks, 2nd Pr, and gutshot draws w/ high card, and less than premium flush draws, I've increased my stack from 50 BBs to 70 BBs, a 40% increase. In the event that I get called, villain is getting bad odds, 50 BBs to win a pot of 70 BBs, and probably won't call me with less than a premium hand, a strong king, two pair, a set, or a bigger flush draw. Were I to open-check here, and there is a bet and a reraise, I have lost all fold equity, and if I decide to jam I can count on going to a showdown, as I can't give people bad enough pot odds
to fold. Even if there's no raise, and it's just a 15 BB bet, when villain is getting 85:35, or about 2.45:1, he's much more likely to look me up, and people being calling after his action just sweeten the pot for him, and others in it.
Of course, in the event that you improve and end up having the strongest hand and taking down the pot at showdown, you'll be happy you got some action, putting your stack at 120 BBs instead of the 70 BBs before. However, provided you are short stack in the hand, your tournament life is at risk. If you are better than your opponents, there is a better time to make a move. If the bubble approaches, you can expect folds from less than big hands. And I don't know enough about ICM to make a strong point here other than, but a 70 BB stack isn't as likely to do as well as a 120 BB stack.
Another option when you get the 15 BB bet is to call. But if you don't improve on the turn, not only do you lose half your equity, but you lose a large amount of your fold equity as well (barring a scare card comes out for villain that fits into the story you've told through your actions, assuming your villain operates on that level of thinking and sees more than just his two hole cards and the board, but that's assuming a lot...)
So if I go busto in a cash game in a hand such as the above at a weak table, I've got more cash in my BR so I'm happy to buy back in, and continue forcing the villains to make bad decisions, and reaping the rewards of my efforts. In a tournament, I only get to go busto once, so I can either take a shot early, or wait until my chances are more solidified and get in with a better edge, because once you account for the 16-20 cards dealt as hole cards, provided a FR table (up to 10), you're looking at 3-6 spades, and maybe a couple of your straight outs, if not more, eaten up. I'd probably be looking for better places to make a play, especially if my table was full of weak (but lucky) players. In a cash game, I'd be stacking off against anybody I felt was made without a better flush draw, and being happy about it. (With the occaisonal passive play while I try to connect cheaply, depending on stack size and villain's tendancies.)
Of course, all these are for playing a pot out of position, and I already feel like I've wrote an essay, and the only tournament stack size I've looked at is 50 BBs. And only one type of hand, being an open ended combo draw...
But these are just some examples. As always, there are tons of factors. Villains, your cards, their cards, the gap in skill, the gap in luck, how you do in certain, what leaks you have, what leaks your opponents are able to exploit, etc.
To answer OP's original question, tournaments and cash games are two different beasts. Depending on whether you play live or on-line will make a difference (my live game is much better than my online game, in one I'm a consistant winner and the other a consistant loser), but that's not for me to discuss at the moment.
I've taken enough time writing this overly long and very specific answer to a general question.