When it comes to sound cards and DOS games things are divided as follows:
Digital sound
The most supported sound cards are the Sound Blaster family. Most ISA cards from the mid-90s try to be compatible with the Sound Blaster Pro. Just FYI SB16 is not fully SBPro compatible, so don't mix them (selecting the wrong one) up when setting up a game. Since SBPro is 8-bit sound only, with a maximum sample rate of 22kHz, many late compatible cards also offer WSS (Windows Sound System) compatibility, which allows up to 16-bit 48KHz sounds to be used. Not many games support WSS though.
Music
This is where things get a bit more interesting. The most common way people experienced BGM back in the day was through FM synthesis. Earlier cards had discrete chips - with Yamaha's OPL2 and OPL3 being the true standard (the original chips used by AdLib and Sound Blasters). Compatible cards with discrete FM chips would either use true OPL chips (like the one from the first post), or "clone" chips to cut costs. Those clone chips sound different (worse) than the true OPL chips. Some can be passable, some not.
Later cards, like some SB16/AWE variants, feature an FM synth core integrated into its main chips. Aside from one chip from Creative (FM synth licensed from Yamaha themselves), most integrated FM cores were clones. Creative had CQM (mostly passable), ESS had ESFM (usually regarded as the best clone) and Crystal and OPTi also had theirs, though those are widely regarded as crap.
Besides FM synthesis if one had the money back in the day to either buy a daughterboard, an external module, or a MIDI ISA card you could opt for another type of synthesis. In the "beggining" Roland's MT32 was used by many devs to compose their songs (which were later ported to OPL), so the older games include the MT-32 tracks. Once GM was stablished game devs switched to using GM Roland modules to compose their songs - and include those tracks in their games. Unlike the vendor-specific MT32, GM was a universal standard so synths from various vendors can be used to playback GM MIDI tunes. All daughterboards for the WaveBlaster header are GM compatible (GM had already replaced MT32 as the de-facto standard by then). Roland's original interface to communicate between PCs and external synths was the MPU-401, and most cards capable of using daughterboards or external modules are compatible with in (in UART mode - which is all GM games ever need).
GM is something to be used instead of FM synthesis for games that support it. Completly optional, but usually sounds better. Daughterboards/modules from different vendors will sound different, which is not necessarily a bad thing as you can have different "favours" of the same tunes.
