Sometimes the term semi is used to describe the whole thing.

Oh Nitpicker of Nitpickers, no one I know or have known calls it a tractor trailer, while that may be technically correct. For example, when it's bearing down on you on the highway, the first words that come to mind is "Watch out - there's a semi passing us!"

So I submit that there are:

(1) technical definition: the trailer only, with the little legs for resting when it's rig-less
(2) practical definition: the whole darn thing, rig/cab, trailer included, even if you find out after it's passed you on a narrow highway and scared the bejeezus out of you that it actually had all the wheels and no little legs