In North American casinos, the unadorned term "Omaha" typically refers to the high-low split variant played with fixed limits also called "Omaha eight-or-better", "Omaha Hi-Lo" or "Omaha8" while the original game is more commonly known as "Omaha High Only". In Europe, "Omaha" still typically refers to the high version of the game, usually played pot limit (sometimes abbreviated as "PLO"). Pot-limit and no-limit Omaha eight-or-better can be found in some casinos and online, though no-limit is more rare.
It is often said that Omaha is a game of the 'nuts', i.e. the best possible high or low hand, because it frequently takes "the nuts" to win a showdown. It is also a game where between the cards in his hand and the community cards a player may have drawing possibilities to multiple different types of holdings. For example, a player may have both a draw to a flush and a full house using different combinations of cards. At times, the players themselves have trouble figuring out what draws and possibilities that their cards hold.
The basic differences between Omaha and Texas hold 'em are these: first, each player is dealt four cards to his private hand instead of two. The betting rounds and layout of community cards are identical. At showdown, each player's hand is the best five-card hand he can make from exactly three of the five cards on the board, plus exactly two of his own cards. Unlike Texas hold 'em, a player cannot play only one of his cards with four of the board, nor can he play the board, nor play three from his hand and two from the board, or any other combination. Each player must play exactly two of his own cards with exactly three of the community cards.