I was just as confused, but figured this all out last month....here is the way it works for the 7100g...
The "browser" on the main page is not an actual application but a shortcut just like the icons on your PC desktop are. It simply points to your default browser, which is the browser you choose in the "browser" options under "settings". In addition to this, all the different browsers you have on your handheld are listed under "applications".
For Cingular Blue (AT&T) customers, the phone comes with the mMode browser (wap). In addition, you can choose to send the BlackBerry Browser service book from the Web Client and it should then download the "BlackBerry Browser" (html). You can then choose which one you want to be the default browser and that will be the one you get when you choose "browser" from the main menu. But both browsers will be listed individually under "applications".
The only disadvantage I have found of not having the "BlackBerry Browser" is that the "Blackberry Extras" website does not load the flash version, but only the b&w version. This is obviously not a limitation of the Cingular Browser since my desktop IE browser does not load the flash version either. It seems that the Blackberry Extras website only loads the flash version on the Blackberry Browser. So other than this, the Cingular Browser appears just as good.