They are based on the same concept, placing cards a on a grid and trying to overturn other lower value cards based on the numbers designated to the cards but the actual rules of doing these "battles" is very different and what ultimately makes fans go to one over another.

Triple Triad for instance had several rules that could be in place to effect the usefulness of a card. When you get rules like Same and Plus, suddenly, some of those old seemingly "worthless" level one cards can now take down high level decks depending on how well you use it. Triple Triad kind of had the best design in terms of "easy to use, difficult to master" which made the game really fun until Random reels it's ugly head. The fact your could refine cards into high level items and the two really cool side-quests associated with it, also help make it a pretty fun game that engages the player from beginning to end.

Tetra Master is a bit different. In some ways it's simpler than Triple Triad since it kind of ignores the rule system, but then it kind of overly complicates things from TT by changing around the value system, and then proceeding to never explain how the value system works. Basically, if you look at a TM card, they have classes that denote melee, magic, and other, but never quite explain how these stats factor into battle against cross values. Obviously if two cards duel with the same class types duel, whichever card has the higher value wins, but then it gets a bit complicated when a card with a high magic value suddenly loses to a card with low melee. The game never really bothers to explain what all the numbers on the cards mean, making the game often feel really random when you suddenly lose an entire hand with your deck of rare cards against a guy using a more modest deck. TM isn't a bad game, but it's lack of meaningful explanation, it's interface that makes reading some of the values difficult if you don't own a sizable screen on your TV, and the fact it's not really relevant for anything but maybe one event makes it more of a distraction than a fun mini-game worth doing.

I prefer Triple Triad, it has a lot more strategy and depth, whereas TM can often be won by just abusing cards with lots of arrows and seemingly high stats. Often, I felt TM could be won simply by making sure you go last in a round, whereas it's pretty easy to shut-out an opponent in TT so they have no chance of regaining the momentum of battle.