Bullet is not a round. Bullet is a part
of a round, the part that flies out of a barrel - a projectile. Same for slugs - they are projectiles and can be found inside shotgun shells. Usually people simply say “slug” instead of using long-winded phrases like “slug shell” or “shotgun shell with a slug in it”, but technically this is incorrect.
Aside from typical ammo with bullets, slugs and shot, there are “crossovers”. E.g. ratshot rounds for rifled firearms, or adapters which allow firing rifle/pistol rounds from shotguns.
More atypical ammo exists, but is rare. Examples include flechettes and sub-caliber SLAP rounds. Frangible rounds also exist, but they are more variants of bullets/slugs/shot rather than entirely new types of projectiles.
At the end of the day, all of them are pieces of metal fired from a barrel to make holes in things. If you exclude explosives and less/non-lethal ammo, there isn’t much variety.