While deck building games are the most familiar of the pool building games, they are just a sub-category of a much larger group. The pool building game mechanic includes any game in which players collect items to build a more powerful hand, and these elements are cycled through in a more-or-less random fashion.
In deck building games players either draft or purchase cards which are then shuffled into a deck to randomize them; cards are then drawn and played. This allows players to customize decks to fit their own style of play, and often gives rise to the primary conflict of the game: competing for the best cards. Dominion, Ascension, and Star Realms are popular deck building games.
The most common alternate form of randomization involves a bag in which game pieces are dropped, and then drawn randomly. In this case the pieces are almost always specialized dice (as in Dice Masters and Quarriors) or chips/tokens (as in Orléans, Puzzle Strike or The Quacks of Quedlinburg). This may also include colored cubes (as in Automobiles), and could include meeple or marbles, although I am not currently aware of any games that use these. These are sometimes called bag building games.
Card building games generally emphasize the ability of cards to be heavily individualized and contain specific instructions; you do not need a look-up table to know what a card does, because the card can tell you what it does. Cards are also very cheap, so it's easy to produce a deck with dozens or hundreds of different cards. This allows for increased complexity without overwhelming the players.
Dice building games are a bit rare; they allow for double randomization, as you draw randomly and then roll the dice. Currently, dice builders have tended to focus on rolling stats for battle, either PvP or against game monsters, and this has somewhat limited their use among board gamers as a whole. The main feature of dice builders is that dice are cool, and the main downside is that dice are expensive. Generally, you can get equally engaging game mechanics from a cheaper game build.
Token-based bag builders are increasingly popular. They provide a tactile experience, and they allow for quick and easy randomization without the wear, tear, and time of shuffling, thus allowing for a new item to be added to the pool with next to no fuss. Tokens work especially well when there are only 4-6 different elements that need to be tracked (more than that and you will need those look-up tables). Tokens have the benefit that they may be used as game pieces and synergize well with traditional board games, and played tokens are often left in play rather than reshuffled/rerolled immediately. I personally suspect that humans are better at mentally tallying small physical items than they are cards, making tracking probabilities and possible payoff a bit easier.
Pool building games are not limited to bags and decks, although it is harder to effectively randomize a pool of tiles or non-identical pieces. It should be quite easy to work around this: e.g., you could draft or buy a collection of diverse figurines, and then find out which one you were using this round by rolling a die. I am uncertain if work-arounds like this are under-used, or if I simple have not come across them.