Everyone else answered your question pretty well ("no, open-source is not a subset..."); I'd like to address a couple of related points.
The reason (or at least a reason) much open-source software is available on Linux as well as Windows and other platforms is due to its open-source nature; say a program exists in Linux, someone comes along and says "Boy! It would be nice if I could use this Linux app while I'm in Windows..." and, with a bit of motivation, they can look at that source code and change it so that it will compile and run on Windows. In a strange, somewhat-recursive way, this can also work the other way around when it comes to "clones" of proprietary software: for instance, I believe LAME ("Lame Ain't an MP3 Encoder") started off as a FOSS solution to the need for mp3 codecs in Linux, but is also now available for Windows, too.
Also, as SL6-A1000 says, you aren't required (though perhaps somewhat peer-encouraged ) to become a full-on Linux-using, M$-hating geek. Many people keep Windows around for gaming or professional needs, even if a Linux alternative is available, for several reasons. If you do come to use Linux and open-source software more often and become involved in the open-source community (or even eavesdrop often, like I do), you will find that open-source is not just a financial or hipster choice; there is a philosophical backing (several, in fact, as hinted at by elija's GPL/BSD comment) for why they do what they do.