Just would like to make clear, I cannot find straight answer. C# is general specification of this language done by MS, while Visual C# is implementation of this language, again done by MS?
So if we say we develop in C# (in visual studio e.g.) we develop in Visual C# actually.
Is that correct?
Yes, you've pretty much got it. Most of us just refer to it as C# though, since it is after all a Microsoft thing, and their implementation of the language is what most coders use (in Visual Studio).
An example of a C# compiler that is not Visual C# is the Mono compiler. The IDE that uses that compiler is MonoDevelop. Both are not Microsoft products, but do implement the C# programming language (as well as the CLR).