Sega's SG-1000 was the competitor to Nintendo's Famicom. It was then updated, restyled and renamed the SG-1000 II. It received further updates, more tweaks to its appearance and was dubbed the Mark III.
That's a little misleading.
SG-1000 was Sega's first console and is basically a Collecovision. Different models have names like SG-3000 and Mark II, but they're all variants of this single generation of console.
The "Sega Mark III" is an entirely new generation of console. It is the Japanese version of the Sega Master System brand. The name sounds like another revision of the SG-1000, but it's not. Further adding to the confusion for gaijins is that the ultimate revision of the Sega Mark III is title the "Sega Master System" and its shell and box looks like the Western SMS. It has the FM Sound, 3D glasses port and rapid fire built-in.
All Sega Mark III systems are backwards compatible with SG-1000 games, which use the same style carts and cards.