So you want to start a magazine. Kindly explain your vision, if you please. These three classifications may generally be arrived at by looking at a magazine's rate of pay to its contributors, frequency of publication, and size of press run. Fanzines pay in copies, publish when it's convenient for the publisher to do so, and survive by word of mouth. You can do a fanzine for darn near nothing these days, given the current state of desktop publishing and on-demand printing.
Tangent is one.
The New York Review of Science Fiction is another. Factsheet Five may be a third. Just keep in mind the value of free advice and you'll be fine. They often get away with much smaller press runs due to lack of significant newsstand distribution. Prozines pay top rates, technically three cents a word but realistically more like seven to ten, if they want decent material.