A term that typically refers to the money/betting aspect of a game is the game's limit. High-limit games are ones that involve a lot of money. Low-limit games are the opposite. As far as how the betting amounts go we have...

Structured Limit
This means that the amount that can be bet is set. These games will be called things like $1/$2 or $20/$40 games. In Texas Holdem, the amount that can be bet pre-flop or on the flop is the first number. In a $5/$10 game, you'll be betting $5 at a time. On the turn and river, the amount doubles. In that same $5/$10 game, players bet $10 at a time after the turn card is dealt.
There is a limit of four bets per player per betting round. That means a player can bet, get re-raised, re-raise again, and be re-raised.
You may encounter a structured game with three betting amounts, like $5/$10/$20. This is the same as before except on the river. On that round of betting, players can bet either of the two final amounts. In the case of a $5/$10/$20 game, that means a player can bet $10 or $20 on the river.

Spread Limit
This is where players can bet within a certain range of amounts. In a $1-$5 game, a player can bet between $1 and $5 during any betting round.
If there are four amounts, like $1-$5-$10-$10, that means you can bet between $1 and $5 pre-flop and on the flop. On the turn it goes up to the 3rd number (between $1 and $10), and on the river it goes up to the last number (between $1 and $10).
If there are three amounts, like $1-$5-$10, that means that you can bet from $1 to $5 during any betting round, but on the river you can bet between $1 and $10. This would be the same as a $1-$5-$5-$10 game.