There's a version table on Wikipedia, probably.

The history of DOS is actually really complicated, arguably even moreso than UNIX, so apologies for the mess I'm about to throw upon you. Because, before we can even talk about DOS, we need to talk about two other technologies IBM wanted in their new PC: CP/M and BASIC. CP/M was the closest thing to a standard disk operating system in the microcomputer world, and BASIC was the JavaScript of the 1980s. IBM absolutely needed both if they wanted to sell computers.

Microsoft was involved with the IBM PC because IBM needed a BASIC interpreter. The OS would have come from Digital Research. But, there was a problem: IBM wanted to use Intel's 8088 chip. CP/M only worked on the incompatible[0], older 8080, and CP/M-86 had been delayed for so long that a company called Seattle Computer Products (SCP[1]) started writing their own 8086 DOS instead. They called it the Quick and Dirty Operating System (QDOS). Bill Gates got wind of IBM's OS problems, bought SCP and QDOS, and sold it to IBM so the PC could ship on time with an OS: "The IBM Personal Computer DOS", or "PC-DOS".

So, to answer your first question strictly; PC-DOS was not made for IBM. It was made for SCP's own S-100 machines first. However, in a sense, it was made for IBM, in that Microsoft made plenty of customizations for them and it contains drivers specific to IBM machines. Bill Gates stipulated that they'd retain ownership of the OS; but the intended licensing model was for other PC vendors to buy the source code and customize it to their own, incompatible architectures. This was the licensing model CP/M used[2]; such a machine would be DOS-compatible but not run any IBM software.

Later on, of course, Compaq was able to legally reimplement the IBM BIOS, creating an "IBM-compatible" machine; and then everyone else in the industry figured out how to do the same and drastically undercut IBM. So MS-DOS was eventually turned from an OEM licensable into a consumer software product that would work on a "standard PC". Digital Research also got into the consumer OS market with DR-DOS, which Microsoft contemplated killing through underhanded tactics[3] but was able to outcompete by better OEM relationships. There's also legally distinct reimplementations of MS-DOS itself, such as DIP-DOS, X-DOS, and later FreeDOS.

[0] Blame Federico Faggin jumping ship and taking the patents with him. Or the Intel manager who demanded he show up to work on time.

[1] Not a front for the SCP Foundation. Or, at least that's what THEY want you to know!

[2] This licensing model also persisted into early Windows; there are special OEM versions of Windows 1.0 that run on Zenith Data Systems machines. It's also the reason why OS/2 1.x comes in "IBM" and "Microsoft" flavors. Microsoft OS/2 was more of a devkit for OEMs who were expected to customize OS/2 in the same way that they were supposed to customize DOS. But it also shipped with technologies that IBM OS/2 didn't have, like LADDR - pluggable disk I/O drivers that would later be reworked into Windows 95.

I should also note that the "DOS-compatible" business model looks a lot like Android fragmentation if you squint at it a little. Remember how I said this was more complicated than UNIX?

[3] The idea was to have Windows 2 or 3 throw fake, non-fatal error messages at the user if it was running on DR-DOS.