Net Standard is a specification of APIs. So in order to be compliant to the standard you must have a class named X with parameters string Y, int Z.
"Net Framework" is the name for the Windows "full .net framework" -- this doesn't have a descriptive name since it was before all the rest, but basically its an SDK that is a superset of the Net Standard (and therefore is .Net Standard compliant / interoperable)
Mono is a open source implementation of "Net Framework" that runs on multiple platforms (linux, etc). It attempts to treat full .NET Framework's surface area as a spec but re-implement it cross platform. It is _also_ a open source CLI implementation. So in common speech "mono" like ".net" can refer to either the "basic sdk" _or_ the runtime environment.
Xamarin is forks of mono for iOS, Android and Mac platforms plus libraries that include full support for interacting with those platforms Native SDKs
Unity is a fork of Mono plus gaming tooling and runtime tools. Microsoft does not maintain this, it's a separate company.