It gets confusing, so I'm sticking to the original definition: a ship is a vessel with three or more main square-rigged masts.
And no fore-and-aft masts. A three master with one fore-and-aft mast is a bark, and with two is a barkentine (I remember that rule holding for 4 and more masts as well, but that may have been from just the one source -- to be fair, the nomenclature tended to break down with really big, unique, ships).
As we are discussing commercial vessels, barks and barkentines required much smaller crews than full ships. I assume, since clipper ships were all ship-rigged, that they were faster for a given sail size (providing that a viable broad reaching course existed, of course) or else everyone would have sailed big dhows for everything.