Difference in source of magic.
While a difference in attitude to magic and the flavor around that could be enough I would argue that I would mechanically focus on the difference in the source of their magic/power.
A wizard would use the raw inner force of magic as learned from books and experimentation. While the cleric would draw power from his/her own belief in a concept (not a god per se) and the belief of others.
In pure Fudge you can apply this by setting the target difficulty level of the spell roll an extra step up or down based on the environment like the wizard going a step up if the area has had it's magic drained or down standing on a lay line. While a cleric spell roll difficulty level would go up if standing in location where satanic rituals are preformed and go down in an church.
If you do not mind borrowing the Aspect mechanic from the Fate system you can use that to let players tap into their appropriate magic for their spells. This would mean that the wizard and cleric would be able to tag different aspects.
For instance a wizard would benefit from an "ley line" aspect he discovered earlier to be able to power up his/her spells while a Cleric could use an "solemn devotion" aspect of a church to power up his spell casting.