Earlier quoted context omitted.
You're probably right. I would still agree with the parent in that they feel like a badly done webview wrapper, because the symptoms are so similar. iTunes Store, App Store, MAS, Apple Music — there is definitely a pattern there, at least on the desktop. I find them all similarly clunky, slow, ugly and unpleasant to use. Apple almost seems to be inherently incapable of creating a decent store front, and I am curious…
The pattern is because they're the exact same app. All of those are just the iTunes Store, which is a web page on every platform. The iTunes Store is a little clunky but it works fine. Apple also have the Apple Store, which is a separate thing that's a website - I believe it's a WebObjects app and the iTunes Store is as well.
This might have changed since they rolled the store into the main apple.com site, but as far as I know none of that is public for sure.