In Omaha you get dealt 4 cards but you can only EVER use 2 cards from your hand and 3 cards from the board. (Say KKKKA comes up on the board and you have QQ43 you have Kings full of Queens, not four kings). If four clubs come up and you have one club in your hand you don't have a flush because you must have two clubs in your hand (and use the best 3 on the board).
In Hold'em you get dealt 2 cards but can play both, one, or neither depending what comes up on the board. (Say AKQJT comes up and you have 73 you still have an ace-high straight).
As for the differences in play in hold'em it is more difficult to make a hand - Omaha you are essentially playing six hold'em
hands with each hand (multiply that by 6 or 9 players and you will can see why the winning hand is often close to 'the nuts' a lot of the time).
Definitely practice on play money tables before playing for
real money!
Good luck to you!