Edge is built into Windows at a lower level than UWP. It is UWP-like in the sense that it has the modern app UX on all Microsoft products, it uses the new APPX package format, it favors the new WinRT API, it uses the new AppContainer sandbox, etc. But Edge can also do things that UWP apps can't do, such as being bloody uninstallable, running executable files, and creating special AppContainers[1].
I should also mention that UWP and Win32 aren't mutually exclusive; UWP is an overarching framework that supports WinRT and a subset of Win32 (now called the Windows API).[2] Edge uses some of the Win32 API as well.
I should also mention that UWP and Win32 aren't mutually exclusive; UWP is an overarching framework that supports WinRT and a subset of Win32 (now called the Windows API).[2] Edge uses some of the Win32 API as well.
[1] https://blogs.windows.com/msedgedev/2017/03/23/strengthening...
[2] https://msdn.microsoft.com/en-us/library/windows/apps/br2057...