On the most smaller mixing consoles, the bass and treble bands of the channel strip eq are made as shelving filters. Some software mixers allow this too. A bandpass lets through only frequencies inside the band while the bandstop does the opposite, it prevents frequencies inside the band. A really extreme version of the bandstop is the notch filter, which, when done right, completely removes all content on a very small frequency band. Those kinds of filters can be hardly audible, but very valuable when you want to get rid of, for example, 50Hz line hum.
Feedback suppressors work with notch filters, too.
Graphic equalisers Graphic equalisers have a certain number of eq bands, of which only one parameter, the gain, is user-adjustable. The other parameters, like Q or frequency, are fixed. Common uses for graphic eqs are as a master eq in a live PA, to adjust the overall sound, or as a master eq on the whole stereo mix. So you can adjust the center frequency of the filter and the gain, but not the bandwidth, which is fixed. How many bands you have depends on the console.