IBM wanted an OS for a microcomputer (what they called PCs then), but didn't have one. They approached a few people and they didn't want to deal. IBM approached Bill Gates, he went out and bought the rights to the OS someone else had written and made a few changes then licensed it to IBM to use. Bill Gates did NOT write PC-DOS or MS-DOS but bought it and made a few minor changes. Gates then had others make improvements to have the later versions come out.

OS/2 was a much later development done as a joint effort until Gates walked away from it, taking most of the code as well and using that to create Windows NT, the basis for the current versions of Windows.