C++ and C# are completely different languages with completely different API and libraries. They share some syntactic conventions at the low level (e.g. basic control structures look mostly the same), and C# is certainly in the C "family", but beyond that they're not terribly similar.
You're not just going to be able to throw your C++ code at a C# compiler with a few modifications. Depending on how much of C++ you use, you may or may not even be able to do a class-by-class port manually. Most notably, C# generics are less powerful than C++ templates, C# lacks multiple inheritance, and C# does not provide predictable object lifecycle for all objects.
The most salient features of C# are the large and featureful standard library, the garbage collector, anonymous methods, and language level support for some standard patterns (e.g. IEnumerable is supported by foreach and linq, IDisposable is supported by using, ...). Day-to-day, these things make a huge difference.
It's completely worthwhile to learn. While C++ provides more control over low-level details, often provides more predictable performance, and has more powerful metaprogramming facilities (templates, c style macros), for most of the code you write day-to-day, C# will make you more productive.
The filename extension for C# is usually .cs.