Think of your wizard as your high damage dealer. There are three types of wizards: fire, ice and earth, with the first two being the most common types. Fire wizards are your ranged damage dealers (and I'm speaking in somewhat generalizations) with fire bolts and direct damage type spells. Ice wizards cast damage spells geared to more in your face fighting. They use PBAOE (point blank area of effect) spells that do some of the most damage in the game, as well as AOE spells that when cast, damage enemies in the area of the enemy of which they are cast on. Earth wizards use damage over time spells and gtaoe (ground target area of effect) spells as well as a few ranged bolts. All of these wizards have access to baseline spells of each path, giving access to some lower damage DDs and bolts, as well as roots, snares and debuffs.
Theurgists carry with them the ability to create their own small armies through the summoning of elemental creatures, commonly referred to as “pets.” The Theurgist can deal direct damage on the enemy as well as pummel him with a small army of elementals. Summoning elementals one after the other, Theurgists hit their enemies from all sides, thus confusing them in the heat of battle. They have the ability to buff several aspects of their realm-mates. Hasting weapons and increasing the damage done by each swing are just two of the ways that Theurgists add to a group's buffing efforts. Theurgists who specialize in earth are often sought out for their bladeturn spell, which helps absorb several swings from enemy weapons and arrows. Their three paths are Earth (very group supportive, pulsing group bladeturn chants and debuffs), Ice (more of a solo type, damage and snare spells as well as aoe roots), and Air (a mix of both, being able to do ice DD spells and have access to mez spells). Again, theurgists have access to all three base line paths as they level up.