Basically CLR is the runtime engine in .NET which handles many things internally which are related to codebase like Thread Management, Type Checking, Garbage Collection, Memory Mangement and many more.

CoreCLR is the . NET execution engine in . NET Core, performing functions such as garbage collection and compilation to machine code. . NET Core is a modular implementation of . NET that can be used as the base stack for a wide variety of scenarios, today scaling from console utilities to web apps in the cloud.