As per the description of Shillelagh it states that the casters spellcasting stat is used for attack and damage rolls for the stick of whatever type. So the question is does the spell grant a bonus to damage based on the casting attribute of the caster ie. Wisdom for druid, Charisma for Warlock if they acqired it via Pact of the Tome? 

EDIT I Believe it does as it states for damage rolls and as an attack cantrip it does exactly the same at level 1 or level 20

It's not a bonus per se, it's a trade. Wherever in the to-hit calculation or the attack damage calculation you'd use STR, you use WIS/CHA/INT instead. So if you have a better mod in those than you do in STR (which as a spellcaster, you should, but you might not if you're a strength-based character who took Pact of the Tome or Magic Initiate) then it increases the damage, but you don't get strength AND you spellcasting mod.

Damage with a quarterstaff in one hand will do 1d6 + STR + proficiency modifier normally.

Damage with a quarterstaff in one hand that has Shillelagh cast on it will do 1d8 + WIS (spellcasting modifier) + proficiency modifier. 

Similarly, attack rolls will simply replace the STR modifier with WIS, or your spellcasting modifier. You do not add anything ‘extra’ to the rolls.

I was just elaborating on what pocketmouse said. Just to clear it up and make sure that there’s no confusion

Quote from VanZoeren >>

Damage with a quarterstaff in one hand will do 1d6 + STR + proficiency modifier normally.

Damage with a quarterstaff in one hand that has Shillelagh cast on it will do 1d8 + WIS (spellcasting modifier) + proficiency modifier. 

Similarly, attack rolls will simply replace the STR modifier with WIS, or your spellcasting modifier. You do not add anything ‘extra’ to the rolls.

I was just elaborating on what pocketmouse said. Just to clear it up and make sure that there’s no confusion

 You don't add your proficiency modifier to damage rolls, only attack rolls, otherwise what you wrote is correct.

I knew you didn't get both strength and casting stat, I also knew no Proficiency mod to damage. I just wanted a clarification on it. Thank you all, and have a great weekend.

Quote from swamp_slug >>

 You don't add your proficiency modifier to damage rolls, only attack rolls, otherwise what you wrote is correct.

 Uh oh! Nice catch, thanks for that. I guess I wasn’t thinking. Hopefully I didn’t cause any more confusion in my attempt to eliminate it!