ASP.NET Core is a web framework, building on top of .NET Core.
.NET Core is a set of libraries and a runtime, with which you can build any type of application (and on which ASP.NET Core is built).
The two projects are related, but have different release schedules.
.NET Core and the .NET Framework are, at this time, different implementations of an API - called .NET Standard (it is a general purpose API, intended for cross platform development). Both are free to add to this API, but are required to adhere to it at least. Again - the standard is versioned, and a specific version of .NET Core and the .NET Framework are expected to adhere to a specific version of the standard.