After the (relative) success of the MSX 1 computer (in Japan, Europe and South America), Microsoft and ASCII presented its successor. The main new feature was the very enhanced graphic modes, no other computers were able to display such graphics! The 128 KB VRAM was very impressive! It had a battery-backed clock and a new MMU (to handle more than the Z80 64KB limit).
The MSX 2 standard, like the MSX 1, was designed by ASCII, the new operating system MSX DOS 2.0 was designed by Microsoft (it's almost a copy of MS-DOS 3.3). A while after launching the MSX 2 standard, Microsoft abandoned the project, but several manufacturers took it over.
John van Poelgeest adds:
As the MSX2 and MSX2+ computers were very alike, it did not take long to have a MSX2 computer rebuilt with the MSX2+ VDP (V9958 from Yamaha) and the BIOS chips from the MSX2+, making the MSX2 computer a fully compatible MSX2+. The one thing lacking was the MSX-Music (FM-Pac), but this could be added by using a cartridge.
Note that MSX-DOS 2 did not ship with any MSX2 by default. It was developed later and sold as an external cartridge (with the kernel) and 3.5" diskette (containing the OS files). The only computer to ship with MSX-DOS 2 was the MSX turboR (both the ST and the GT) which had MSX-DOS version 2.3x built in.