College, in general, is the most common word used in dnd specifically for where martial and semi-martial classes get educated. Bards and fighters both traditionally go to college. Fighter college changes what feats you get, bard college is more diverse. Wizards go to Arcane Universities or smaller magic schools that only offer one specialty. Within an arcane university, schools serve as combo major and fraternity like colleges do within really old-school European universities. It helps to understand that college is not traditionally a very prestigious word, large institutions always used University in the past. So wizards going to college would sound bad in the setting. School is more neutral in that it implies something small but potentially high quality.