What's the difference between c++ and c#??
C# is also a far more modern language than C++, and in many respects it's easier to learn as well. C# is really quite different to C++, it's much more similar to Java (in fact if you know Java, you pretty much know C# once you've taken into account some minor syntactic differences.) As stated above it's specifically geared towards windows as well - whilst you can compile it on *nix machines with tools such as mono, the results aren't always great.
Personally though I'd really recommend starting with Java instead. Follow a good guide (there's lots out there) and it'll teach you strong object oriented principles and you should be able to get to grips with it fairly quickly. It's much easier to learn than C++ and it's more flexible in nature than C# (and due to the fact it's been around a while and is open source there's generally more libraries around for it as well.) It's also one of the most widely used languages out there at present, if you can put down you're a strong Java programmer on your CV then in this industry that'll be a real plus.