It was Sega's very first "console". After that came the SG-3000, then the MarkIII/Master System. It was pretty popular in Japan, as was the 3000, but then the NES came along with Nintendo's monopoly. :rant
SG-1000 II - same as before just updated design (sort of like what happened with Genesis)
SC-3000 - an SG-1000 with the optional keyboard built-in, came out at the same time as the SG-1000 II
Mark III - basically the third version of the SG-1000, identical hardware
Master System - an upgraded SG-1000 with MIDI module (which was removed for North America and Europe), it was completely backwards compatible with all SG-1000 software. In fact some was just repackaged in the new carts and sold again.
midi module's a bit misleading. it's an fm sound chip similar to what was in the genesis. there were only a few games made to support it. the japanese versions of wonderboy 3 and phantasy star come to mind. no euro or american carts support it (obviously) so were you to stick you cherished copy of cuborg hunter in there you'd notice no difference. meka emulates the fm addon and is easily the best sms emulator out there anyway
The FM chip is basically almost identical to the FM chip found on the Sound Blaster family of cards (all the way up to the AWE64). So for that time it made the game sound really good, especially compared to the NES. There was an upgrade module for the MarkIII that would add the FM capabilities to it, basically making it a Master System. North American and probably European games generally retained their FM capabilities but since they never detect the FM chip it doesn't matter.
As for the games about half of the Master System games released in Japan has support for the FM chip. Here is a list of them. Look in the column marked FM, any game with a circle in that column supports the FM chip.