As JW said "a yacht is a
boat, regardless of size, used for pleasure, not
work." and I suspect Chapman's and other standard
references would say the same thing.
But at least here in the states, a "launch" is always something that can be carried aboard and LAUNCHED from a larger vessel. Unless it is reserved for the use of an Admiral, in which case for some reason the USN refers to it as an "admiral's barge" never a launch. (Probably because the Pharoahs used barges.<G>)
Among the boaters I know in the US, a yacht is intentionally refered to as a "Ya-chit" (rhymes with ratchet) and reserved to mean something especially fancy and carrying persons who either are in uniform, or formal sailing attire, or in some other way beyond the casual world of sailing.
IIRC HMS Britannia was formally called the Royal Yacht though, wasn't it? The perils of allowing the Brits to keep speaking
English, instead of taking it as a war prize from them so long ago.<G>