OK I think I can simplify things a little here. I'm probably reiterating a lot other people have said, but I just wanted to lay it all out to make sure everything's clear.
Here is how B&W negative film works. It's pretty much the same for 120 film as well as for normal 35mm film. First, when you expose a shot on a roll of film in your camera, a chemical reaction takes place wherever enough light hits. When you take it to a lab to be developed (or when you develop it yourself), you wash the film with certain chemicals that first: darkens any areas that were exposed on the film (by reacting the chemical with any of the film that reacted to light), second: makes transparent any areas that were not exposed, and third: makes the film no longer light-sensitive (more or less chemically inert). So after development, any areas that were exposed by light become dark, and areas that were not exposed are transparent. Thus you have your negative, since the light areas became dark and the dark areas are light. So to answer one of your questions: indeed, the film that you put in your camera is the same film that you get back from the lab; all the lab does is chemically treat the film to make it useable to make prints.
Color film is a pretty similar process, except the film has multiple layers, each sensitive to a different color. When it's developed, extra steps are added to the end of the process to differentiate the colors.
Using traditional darkroom methods, when you went to make a print, you would put the developed negative in an enlarger and project it onto paper (essential film on a paper base instead of a transparent one). This creates a negative of the negative, producing a positive.
An alternative is of course to use a scanner to make a digital file of the image, allowing you to print on an inkjet printer. I'm sure you understand that part ;-)
Developing your own B&W film is relatively simple, but it's a bit of a tedious and error-prone process. It's even harder with color, as slight variations of development time or temperature will cause noticeable color shifts. You can usually get away with more mistakes when doing B&W. Most of the time if you take it to a good lab you'll get good results, because they have good equipment and trained staff (unless they're not such a good lab). When you do it yourself, you'll likely be more prone to errors. Also, it takes practice to learn to process your own film well, and you'll probably mess up a few rolls from time to time while learning.
And like I mentioned, the development process is the same for 120 film as it is for 35mm. The only main difference is how you load the film onto a reel to process it.
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