I think you'll find that C# is more akin to C++ than C. I also think that C# will take you in different directions than C, since it is Object Oriented and is fully integrated with the .net librairies, including creating windowed GUI's, web-based, and data based applications. Due to it's very basic code, C, I believe, is favored by many of those that do embedded programming.
@S, I'm going to write no. Many years ago before we had C almost everywhere I wrote in assembler. That demanded we know the processor and system to the core. When we moved to C we didn't have to know as much since it's there to remove the requirement to be intimate with the host details or even what CPU was being used.
As to the assumptions, a google search could confirm that.
You can write programs with C. You can even write Windows, Mac, or Linux GUI programs with C. The main disadvantage is that you have to use the native API's for each type of machine, which can create major problems when the OS decides to change the API's you rely on. Another aspect to consider, since C doesn't lend itself to an Object Oriented approach, it's very easy to get into bad programming habits.
If embedded programming is to be your focus, then C is a very good place to start. There are also several good online tutorials that teach using C in embedded programming.
@tinstaafl, this is a really good area where your choice of C or such can matter. That is, picking C for embedded work is one of your best choices since there's a chance others may understand what you did and be able to maintain or fix it later.
We all have stories. One job had a crushing requirement on cost so the cheapest microcontroller was going to be used and it had no RAM. Just registers and a few hundred bytes of flash memory. The task at hand was to add functionality to an existing system that was omitted and the product was already being sold at or below cost. A salvage job. This meant assembler was the choice and it was done but few dared to review that one. Once done the product finally was sold off and the company moved on much the wiser.