I've got a lot of free time in school so I always bring playing cards and poker chips. Also bring some basic stuff like notebook, pens(YES, I COLOR MY NOTATIONS JUDGE ME), energetic bars and a water bottle.
Common between both:
Lunch/food/snacks
Wallet
Water bottle
Keys
Utility/pocket knife
Pens
White board markers
Plastic bags
Medium notebook
Small pocket notebook
Samsung tablet
Phone
Sunglasses
Gum/mints
Deoderant
Sunglasses (If not wearing)
Earphones
Panadol (Not normally but I brought some to work and didn't use it so it's still there)
200mg caffeine tablet (Same thing as above - brought to uni but didn't use)
Exclusive additions to uni:
Relevant books for classes that day
Textbooks if needed
Wider selection of pens/pencils/etc
Laptop
Charger
Sometimes a wireless mouse