TACAN is simply the MIL equivalent of VOR/DME - it was originally supposed to have better accuracy (not sure how true this is in practice with modern receivers and ranges though).
I believe the real reason the MIL wanted a system different to VOR is that it is more "tactical" in that it can be deployed more easily at short notice, in theatre, on un-even surfaces, ships at sea or even on airborne platforms. So TACAN receivers abound in MIL aircraft, and hence MIL airfields typically have TACANs for NAV and/or APP purposes.
VORTAC is simply when an VOR and TACAN are co-located - common in the US.
Andy
