I have 2 questions. When I create a new project using VS2017, I can't use.net Core as Frameworks listed are only for .net f/w. Why is it so?

See below: Project Creation

The next screen asks for the template. While choosing a stateful or stateless service, we have a different template for .net core and .net framework categories but both of them mentions .net core in the name Service Template

2 Answers

LoekD On

The ASP.Net core MVC libraries are .NET standard 2.0 libraries, so you can reference them from any supporting platform.

Including full framework applications and .NET Core applications. More info

SteppingRazor On

As you can see, if you choose to target .NET Framework you can still create ASP.NET Core service and use ASP.NET Core features. That's not a problem. The only downside is if you want your application to be multi platform (for example run on Linux) you cannot do that. You need to target .NET Core instead.