The two you will encounter.
WHAT THEY ARE
The mechanism a table uses to store and retrieve data. Set per table, not per database.
MYISAM
The older default. Faster for simple reads in some cases, and it locks the whole table during a write.
No transactions, no foreign key support, and considerably more prone to corruption after an interrupted write.
INNODB
The modern default. Row-level locking, so writes do not block the whole table. Transactions and crash recovery.
Substantially more reliable.
WHICH YOU SHOULD USE
InnoDB, for essentially everything. Modern applications assume it.
CHECKING
phpMyAdmin's Structure view for the database lists the engine per table.
A site with mixed engines is usually an old installation that was never converted.
CONVERTING
The Operations tab for a table offers a storage engine change.
Back up first. On a large table this takes time and locks it while running.
WHY IT MATTERS PRACTICALLY
MyISAM tables are the ones that get marked as crashed. If corruption recurs on the same table, converting it is frequently the real fix.