A couple of key points IMHO:
1. Cash games $1 = $1. In tournaments, each extra $1 in chips you have is less than $1 in true value... as you know from Harrington (I think that's where I read it). So you generally want to avoid more marginal situations, especially early when your M value (Harrington) is high.
2. In tournament games, you have a limited supply of chips as you pointed out. So you have to be less inclined to play hands like suited middle connectors early. In a cash game, that is not the case and the implied odds
(as Doyle points out in Super System) are thus much more favorable for their play. There is no M value in a cash game, only a Q value (I think that's what Harrington calls it) -- that is your stack size on the table compared to the others at your table. So, if you have a marginal holding like 89 suited and a guy with a large Q (who can double you up) raises and there is a caller also with a large Q, you're much better off calling his raise (Implied Pot Odds
are large) than you are against a guy with 1/4 of your Q value who raises and gets another low Q caller.
There are many other differences, but those are a couple of the key ones I try to remind myself of in those situations.
So to answer one of your questions succinctly, you should play tighter IMHO in a tournament's early stages and looser (or more loose in general in certain situations) in a cash game.