I took "identical" as in feature wise. The user should be able to accomplish the same things, no matter what platform they're using.
I do think that the way the features are implemented should be platform dependent, i.e. use common UX pattern on each platform, fit in with the UI, and be good platform citizens.
The solution is to make the common features a part of a statically-linked library that you can pull into your apps. A web app is, IMO, never the answer when you want to address multiple audiences. It is bad for accessibility (because 99.999 percent of web app developers never consider accessibility) and it doesn't solve the problem that web apps are trying to solve (having 8 code bases all that have to remain in sync) because you will inevitably need your code to handle platform-specific differences, standards/conventions and whatnot.
Why does Shopify need to use Apple's or Google's branded design language in their app?
Because if I’m an iOS user and used to that and you give me a conventional Android app UX, I’m going to feel that as jank.
Same as if I’m an Android user and you give me the conventional iOS experience.
It’s like if I gave a swing or Gtk+ or Xwindows app experience on Windows 11 or MacOS. It would be usable, but feel conspicuously sub-standard.
What specifically are the ux differences?
I don't know iOS so I can't say, but a good UX does depend in part on platform expectations and every system historically been different. The compromises mean the each have good reason for what they do (sometimes anyway), but switching is hard.
I've used both in the past 2 years and can tell you these particular systems aren't meaningfully different in any way that affects third party apps.
It shows the sad state of user experience that applications completely ignore how different platforms function. For websites, I would expect them to follow the web conventions of UX. However, as soon as you're in a "native" application, you need to function like the device you're running on wants to function. Otherwise, it's going to be a jarring user experience for everyone in there. The whole system becomes harder to use.
That's because you must be using cross-platform apps.
I'm only familiar with iOS and this is the type of question that an LLM could answer better than this specific human.