I think you're interpretation of what is Windows 10 may be different from Microsoft's. You are looking from a user perspective, saying that the desktop UI and having Win32 compatibility is required. Microsoft is looking at it from the kernel, drivers and focusing on UWP which is supported on IoT, phone, desktop, Xbox. For them, Win32 is a compatibility layer, more so when you start looking at the vision of Centennial which starts pulling old Win32 apps into a more managed UWP VM.
I don't deny that the average user thinks Windows is a PC with desktop that runs any Win32 legacy app, but I'm not sure that's what Microsoft sees for the future. And for that reason, the phone really is running Windows 10.
First off, let me be clear that I'm not looking at this from a user’s perspective at all. I'm looking at it from the perspective of computer science, and what people working in the field generally feel defines an OS. Most would say that two OSes can only be considered the same if they can run the same software. That's one of the most fundamental requirements, and W10M and W10 don't meet that requirement. Period. As far as I'm concerned, at least from a technical perspective and for the present time, that's the end of same-vs-not-same debate.
I understand you're getting around that definition by declaring millions of Windows software titles (the things Windows users care most about) as obsolete, and by relegating at least 2/3rds of W10 to "compatibility layer" status. In short, you're saying everything that is different is obsolete, so they are the same. I agree that this will someday make sense, but adopting that definition and related terminology today seems very premature to me. I understand that you're ignoring the current reality and looking more at the conceptual idea of where W10 is headed, but currently that mark on the timeline is still quite a ways off.
However, I agree that W10M is the real future of Windows. Some here envision everything eventually just becoming W10 (once an x86 based phone is released), but if anything is eventually phased out, that is far more likely to be W10, not W10M! More precisely, what will be phased out are the many GB's worth of legacy functionality W10 contains, which serve no purpose in a purely UWP based world. Whatever we're left with at that point, and whatever it will be called, it will be a lot closer to today's W10M than today's W10. In regard to this issue I think we're on the same page.
The thing is, we're still many years away from the point of transitioning away from W10. In regard to transitioning, I'd also add that I've never heard of Centennial placing Win32 software in a managed UWP VM. AFAIK Centennial is more accurately described as a combination of run-time file system virtualization and dev-time automated installer repackaging. It doesn't, in any way, allow Win32 software to run on the UWP, so I wouldn't count that as a meaningful step towards getting most Win32 software migrated over to the UWP. Centennial's goal is to make Win32 software distributable through the store. We're nowhere close to the point where we could easily convert Win32 software into universal apps.
In summary, all the things that could/would eventually make it reasonable to give both OSes the same moniker are all still very much in the future. I see no benefit to confusing people by introducing terminology that will be technically inaccurate for many years to come. Why not just introduce that terminology when it actually matches reality?
Anyway, reasoning aside, I understand your fundamental point. AFAIK you could be right about MS (you?) and myself judging what W10 is from different perspectives. Truth is I have no idea what MS thinks the name "W10" does or does not refer to. Based on the fact that MS initially called W10M just W10, then went with W10 for Phones, then settled on W10M, and that we're now seeing some people go back to just W10, I think it's clear that MS are themselves very much lacking a clear idea of what W10 is and what it isn't. They wouldn't have that problem if they'd just stick with a nomenclature that reflects reality as it is today, as I'm trying to do.