About few months ago me and my team have started new project in .net core. We wanted to use the newest technology that is on market (in .net world). After few months we discovered, that not every component in .net ecosystem is written in ".net core way". For example EntityFramework (at this moment there is version EF.core) or WCF (at this moment we still need to use .net 4.6.2).
In one project we have library (.dll) that was used by:
a) .net 4.6.2 solutions (WCF)
b) .net core solutions (our main Web App, tests, and others)
First we used .net core library, after that we have changed to .net 4.6.2 library (and git have problems with branch changes old/new library). But in situations, when we need to use some library in both, .net core and .net 4.6.2 solution there is better way. It's called .NET STANDARD LIBRARY.
.NET STANDARD LIBRARY is a new library type project (.dll) that can be used in many different project types in example: .net 4.6.2, .net core, mobile applications. It have some limitations, but in general this is a big step in good direction.
There is good blog post in MSDN -> https://blogs.msdn.microsoft.com/dotnet/2016/09/26/introducing-net-standard/
If you newer heard about .net standard library you should read about it.