MM = 2000 in roman numerals. We're in the year MMV right now.
In the metric system M = 1 million. So $1M really does mean 1 million, for most of the world ;)
$1k is $1,000 using the metric abbreviation.
For some people MM does mean 1 million, its a confusing term (think of MMBTU, MMBbl). I'm pretty sure it came about because you couldn't type the proper key in with a typewriter (an M with a bar above is the roman symbol for a million). Once upon a time they had to make do typing with only the 26 letters (pre-internet, it was a ghastly time). Its probably an accepted custom because of how typewriters worked. It doesn't make it wrong, it's just an historical anomaly that is now a custom.
so MM=M=one million and the correct term is dependent on context.