Do "super", "hyper", "ultra", "meta" actually mean anything different beyond just being "cool prefixes" that cycle in and out of favor either organically or suddenly when a major entrepreneur just comes along and names their entire ecosystem after one of them?

Hyper- is an allusion to the early Web. 

Hypertext is interconnected with Hyperlinks. They take you from any page on any server to any other page in O(1) clicks.

Hyperchain is interconnected with Hyperbridges. They take you from any address on any ZK chain to any other address in O(1) tx cost.