What's the difference between .NET Core and PCLs?

I was writing up the supported platforms for my PCL recently, one of which is other PCLs. I was confused if my library (which targets .NET Framework 4.5 and Windows/Phone 8.1) can be used in .NET Core projects as well.

As I understand it, PCLs allow you to share code across multiple platforms without recompilation, while .NET Core does that as well. The only difference is that .NET Core targets a few more platforms, i.e. OS X and Linux, and is open source.

So essentially, I don't see how .NET Core is any different than Microsoft rebranding the PCL and going "PAY ATTENTION we're going open source and targeting non-Windows platforms!" (Someone please correct me.)

So the bottom line is, are PCLs compatible with .NET Core, and vice versa? What's the difference between them?

via Chebli Mohamed