Naban, Dean of Iteration

Look at each permanent as it exists on the battlefield, taking into account continuous effects, to determine whether any triggered abilities will trigger multiple times. For example, if you control Arcane Adaptation with Wizard as the chosen creature type, a Runeclaw Bear entering the battlefield will cause any abilities it triggers to trigger an additional time.

Abilities that apply "as [this creature] enters the battlefield," such as choosing a card name with Meddling Mage, are unaffected.

The trigger event doesn't have to specifically refer to "Wizards." For example, an ability that triggers "whenever a creature enters the battlefield under your control" would trigger twice if the entering creature is a Wizard.