Anti-seize is grease PLUS very fine metallic powder, depending on the application; Aluminum, copper, nickel, etc. The powder acts as a layer to prevent seizing and galling, even after the grease dries up. The powder can be abrasive to the bearings. Many grease applications can use anti-seize in a pinch, but not bearings. However many use grease in place of anti-seize.

Also: Grease used to differ based on "sliding contact" (bushings, like in car steering linkage and ball joints), and "rolling contact" (bearings), but most automotive greases now will work for both. I use (greenish-blue) marine wheel bearing grease, used on boat trailers that need to be submerged to pull the boat back on, it's supposed to repel water better; Usually found cheap locally at RV supply shops. A local bike shop that's known for Internal Gear Hub (IGH) service, swears by the stuff. But any good wheel bearing grease will do. Black lithium grease like my dad used to use in the grease gun for suspension bushings, that's a no, if they still make that stuff. Back in that day, wheel bearing grease was called "long-fiber grease" because when you scooped out some, it left a long thread of grease in mid air between your finger and the can of grease.