i am primarily a cash game player.  not a pro or an expert by any means, but i don't usually have the time to play a big tourney, so i play mostly cash games.  this past weekend, i had a very rare occasion where i had a whole night at home to myself.  i couldn't get a home game going, so i decided it was a perfect time to play a tourney.
    for many people starting out in poker, there's not clear line between cash games and tournies as far as how to play the game is concerned.  you still get two cards, there are still five cards or less on the board, and the best hand wins at the showdown.  poker is poker.
    there are many many differences between the two forms.  i find that in full ring game, i play much tighter and rely more heavily on the pots odds.  odds based decisions are usually correct because poker is a long term game, and every session you play at cash tables is essentially a continuation of one big lifelong game.  odds are critical because it gives you peace of mind knowing that if you are 60% favorite to win a hand, that you will make money in the long run, even of you happen to fall into the other 40% on any given day.
   in cash games,you can make money playing straight ABC poker and only playing the top 20% of hands.  if you can develop the skill to pick good spots and take down a few extra pots along the way, you are well on your way.  todd brunson is famously tight at the cash tables, and he is also famously successful.  cash games are potentially steady income if you exercise strict bankroll management and don't tilt too hard whenyou take some hits on the low percentage side of the hands you play.
   my tournament game is somewhat different.  i find that i am far more aggressive in tounraments, especially in position.  i play some hands i wouldn't even consider, and i play them like i have aces until someone gives me a reason to slow down.  there's something about knowing that making a bad call with bottom pair ending your tournament life that makes it hard to call me when i stuff a big re-raise over you in late position. 
    also, there's no reason to ramp up the aggression if you get down to 10 bb's or less in a cash game, unlike a tournament.  because the blinds are constantly going up, you have to constantly build your stack or you risk being blinded away.  for me, with 10 bb's or less, i am going to be open shoving with anything even remotely decent in just about any position.  that would be a terrible play in a cash game, but it's standard tournament strategy.
    blind stealing is essential in tournies.  so are c-bets and, in my version of tournament strategy, raising and re-raising on early streets to find out where you're at in the hand.  do it early and get out if you get any action back at you.  i don't call at all, and i shove my stack whenever i think i can force a better hand to fold. 
    in my not-an-expert opinion, aggression is a hundred times more important in tournaments than it is in cash games.  it's still essential in cash games, don't get me wrong, but with escalating blinds and a build or die mentality, aggression is what separates the successful players from the less than successful players out there.
     those are some of the differences between cash games and tournaments.  there are surely several hundred more differences that i haven't mentioned in this post, but hey, i'm not writing a book here!  lol. 

good luck out there.