I tackled ApplescriptObjC. I started making apps with the interface builder and such. But can you make actual games in ApplescriptObjC like you can in normal Objective-C? What is the difference other than the syntax?
There is no difference. AppleScript-ObjC is a way of speaking to Cocoa using AppleScript instead of Objective-C. Whatever you can do with Cocoa in one language you can do in another language: Objective-C, AppleScript, Swift, whatever.
Some APIs are C APIs, and some calls may work best using C or Objective-C. But in general the matter of language is irrelevant; that is what a "bridge" means.