I've heard the terms "full suspension" and "soft tail" used interchangeably, but I've also heard them used to mean different things. To me, a "soft tail" is something like a Moots YBB or a Salsa Dos Niner, with a tiny ~1"-travel shock mounted at the top of seat stays. A 'full suspension" has 3"+ of rear wheel travel, IMO, and the shock is placed elsewhere in the frame, depending on the style of suspension.

I don't think that either variation is right or wrong...just the different ways that different people use the terms...