There are four races of characters in Ring of Fates, each with unique abilities. Your party in the single-player game will include one of each of these.
This is the character class of Yuri, the main character from the single-player mode. Clavats are strong melee fighters, able to deal impressive damage and execute fast combos. This makes them an ideal class for beginners, as they're definitely the simplest to play and the best equipped early on. Other classes are more of a long term investments. Their tribe ability allows you to touch enemies on the bottom screen for heavy damage; pretty intuitive and versatile. They also get a charge attack that will automatically knock down regular enemies if it connects. This can be very powerful if used strategically.
Selkies are the archers of Ring of Fates. They're fast, nimble, and their doublejump ability helps them to reach places other classes can't. To balance out their long-range attack ability, they are fairly vulnerable to physical attacks. They're often difficult to start out with, especially solo. They eventually learn a 3-way attack at level 13, and later a 5-way shot. At close range this can be used to greatly amplify damage to a single enemy, but more often it just helps for crowd control.
The basic mages of the game, Yukes can actually be half decent fighters in some situations, due to the greater range than melee fighters. They lob orbs of magic damage from their staff which can travel a couple yards. At close range, they can also deal physical strikes on top of this. They have the greatest magic ability, and can lock more rings than other classes (level for level). They sometimes struggle in solo play because it can be difficult to cast large spells without anyone to defend them. Their tribe ability is an interesting one. It uses the touch screen to "spread" the magic from stray Magicites around the screen. This is generally a lot more effective than a simple cast.
The Lilties are alchemists. They have the ability to create new Magicites and materials during the game, which makes them a valuable support class, although the actually alchemy process is a little slow, and in some situations it's easier just to milk enemies that drop what you need. The good news is that Lilties are pretty solid fighters, with good melee attack abilities. They also have some unique abilities thanks to the alchemy pot they can summon, which allows them to roll and fit in places other classes can't.