Basically, all of them can take accuracy and damage but from there things get more diverse.
Some pets can take heal sets, others defense debuffs. Some can take knockback while still others can use immobilize. You'll have to see specifically what sets your pet can take by hovering over each pet in the enhancement window. There it will say what "common" enhancements they can use but also below that what IO sets they can.
Now, as for the difference between Damage Pet IO's and Recharge Pet IO's...
The tier 1, 2 and 3 MM pets cannot use the recharge pet sets, they can only use the regular pet IO's. Those recharge pet IO's are for short duration and/or long recharge pets like Fire Imps and Singularity in the Controller/Dom sets and can even be used for things like Voltaic Sentinel, Tornado and Gun Drone. However, those recharge pet IO's CAN be used in certain MM pets, like Thugs Gangwar and Necro's Soul Extraction.
Just double check each of your powers to be sure what can go where and you'll be fine. Also, if you don't have it yet, download a copy of Mid's Hero designer here.
Hope this helps. 
Losing faith in humanity, one person at a time.
Yep, that wasn't the answer i was hoping for, but it answers to everything. Thanks. =)
Another question, i'm almost sure of the answer but... do the "aura" unique IOs affect the MM too? Or it just gives def/res to the pets?
"It's a scrapper. If he can't handle it, no one can." -BrandX
Those only affect the pets.
Losing faith in humanity, one person at a time.
I'm new to MM and trying to figure out for when i'll be 30.
What kind of sets exactly can you slot in your pets? I keep hearing you can slot every set one of the pet's power could technically slot, but it isn't written anywhere... Is it true?
Also, what's the difference between Damage Pet IOs and Recharge Pet IOs? Can they both be slotted in MMs' pets or the recharge ones only go for temporary pets? (if so, does a lot of primary/secondary have temporary pets?)
"It's a scrapper. If he can't handle it, no one can." -BrandX