Objective-C 2.0 was part of 10.5 in 2007. It’s not directly tied to 64-bit support. You’re thinking of features that require the “modern runtime” which is only available on 64-bit Mac. Those features came after ObjC 2.0.

You're right, I mixed those two up. That's a bit too far back for me :)

"Objective-C 2.0" was a marketing term for a bunch of features added in 10.5, some big (e.g. nonfragile ivars, garbage collection) others not so big (e.g. for..in loops, synthesized ivars). The language+runtime has evolved tremendously since then without a new marketing name. Generics and ARC were added, garbage collection and vtable dispatch have been removed.