Direct 3D is the graphics part of Direct X. Direct X is just Microsoft's bundled A/V API (I think?). Coupled with DirectSound, DirectDraw and DirectMonopoly you can create magnificent things....
(some parts of this information are fiction. some assembly required)
The real defininition:
"A set of APIs developed by Microsoft that enables programmers to write programs that access hardware features of a computer without knowing exactly what hardware will be installed on the machine where the program eventually runs. DirectX achieves this by creating an intermediate layer that translates generic hardware commands into specific commands for particular pieces of hardware. In particular, DirectX lets multimedia applications take advantage of hardware acceleration features supported by graphics accelerators."
Wow! Hardware independent! That's great! Except...errr...well, it's not OS INDEPENDENT... So let's just stick to Open GL as our graphics format of choice.

No reason to give M$ an edge anywhere else. Not to mention, in my opinion OGL has always looked better in the past.