Mozilla has different browsers, and there are actually quite some browsers that are based on Mozilla: Mozilla suite, Seamonkey suite (the same, basically), Firefox, Ice weazel (or something close to that) etc... In addition to those Mozilla-derived browsers there are indeed Opera (which is available for Windows also), Konqueror (KDE's all-in-wonder file manager & browser), Epiphany (for Gnome; again a Mozilla-derivative), Explorer (but only trough Wine, because it's a Windows program!) and so on. Actually if you do a google search for internet browsers for Linux, you'll find more than you want
Mozilla just seems to be a favourite for a lot of people. A little like Opera is for some.