Nope, Visual Studio for Mac started as a rebranded Mono thing after Xamarin acquisition.
Since then, the amount of plugins shared with Visual Studio has increased, which is a reason why Microsoft started pushing to write them in C# instead of COM.
Currently it is being rewritten, and should be mostly completly unrelated to Mono Develop by .NET 7 release.
No, Visual Studio for Macs is a rebranded Mono thing, it has nothing to do with the Windows Visual Studio. There's no VS for Linux.
Of course MS had to complicate things by naming their electron editor Visual Studio Code...