CLR and CLI - What is the difference?

The CLR is Microsoft's implementation of the CLI standard.

CLR is the execution environment in which a .NET application is safely hosted/run.

You can see it as .NET's private Operating System that initiates and loads just before a .NET application starts.

The CLR takes care of certain essential requirements of any .NET application that otherwise would require lot of deliberate code to be written in order to implement; requirements that are holistic in nature and essential to any kind of application to run in a good, efficient and safe manner [e.g. Handle memory allocation and release it when not required, avoid dangling pointers, avoid type-casting errors etc. ]

CLI on the other hand is a specification/set of guidelines that explains how to implement an application execution environment and the nature of generated application code that allows for multiple high-level languages to be used on different computer platforms without being rewritten for specific architectures.

CLI is developed by Microsoft and standardized by ISO and ECMA.

The CLR is a practical implementation of CLI's VES [Virtual Execution System] section and forms one of the core components of the MS.NET platform

In a layman's language, CLI is a recipe while CLR is the cuisine :-)