DME was developed for the military, and is an inherent part of any TACAN or TACAN receiver. The civvies thought it was a good idea and developed their own stand-alone receivers, and also added the DME component of TACAN to many VORs.

1) VOR: VOR only, no DME
2) VORDME: VOR w/ DME
3) VORTAC: VOR w/ TACAN (which includes DME).

2) & 3) are the same as far as civilian aircraft are concerned.

Basically we prefer VORs that have more letters at the end.