My confusion is I read that UWP uses .NET Core, but there's a separate ".NET for UWP" API documentation here. Also, I can't find some .NET Core features in my UWP project.
.NET Core is a cross-platform subset of .NET that can be use to build apps for Windows, Linux, Mac, and yes, UWP.
UWP Api is also a subset of the .NET API, which can run on .NET Core. It also has a number of API's that are unique to UWP. UWP apps can be .NET core apps, but the reverse is not necessarily true. Not all .NET core apps are UWP apps.
Just like there are API's for .NET Core that only apply to Linux, or Mac.