Windows 2000 sold as both a server OS and a workstation OS, but there was no home edition of 2000. There was also no professional version of Me. It would probably be more accurate to say there were two separate paths of evolution that converged with XP.
NT -> 2000 -> XP
98 -> ME -> XP
Though, XP is built off of the NT kernel, so you could also argue that the 9X line ended with ME.
Yep. In the beginning there were two threads of Windows garbage: Win NT (for companies, with NT kernel) and (MSDOS-based) Win 9x for peasants.
Win 2000 was the "last" Win NT and Win Me was the last Win 9x.
That's not 100% true as Me used something called "Real mode DOS" which limited the OS interactions with DOS and Windows XP was an evolution of the NT kernel, and all subsequent windowses come from that kernel (Vista, 7, 8, etc.. and the Server variants).
Win Me was the "Mistake Edition" because it was half-baked, most of Microsoft was focusing by then on the next iteration of NT and they even didn't ship to developers the Me version but rather Windows 2000.
And probably Windows Me was on the knowing about 9/11:
"System Restore suffered from a bug in the date-stamping functionality that could cause System Restore to incorrectly date-stamp snapshots that were taken after September 8, 2001. This could prevent System Restore from locating these snapshots and cause the system restore process to fail. Microsoft released an update to fix this problem."
2000 was the first Windows with an NT kernel that was really usable on the desktop. Some may argue NT 4 but in 2000 almost everything worked as expected. XP was clearly better of course.
But you're right - ME was actually a successor to 98 and XP was the joint successor to 2000 and ME.