Barbarian Wild Magic only happens when you enter Rage, which at maximum is 4 times per day assuming pure Barb. Sorcerer it happens as a chance any time you cast a level 1+ spell; well you get a lot of spell slots on Sorc.

Surges are random magical effects that occur on or around the caster at the moment they cast a spell. The frequency of surges and chance of good or bad results can be manipulated by things in the wild mage tree (sorcerer) Surges are divided into five categories: Very Good (chance is very rare)

Wild Magic is one of the Subclasses of Sorcerer. These Sorcerers are capable of using the chaos of their magic to unleash various unexpected effects that can be helpful or chaotic. They also have the ability to gain Advantage on rolls, in exchange for their magic becoming more erratic and surging more often.