If you want to be really pedantic, "swell" is the movement of the sea, generally that remaining from rougher waves far away. Waves are.. well, just waves, caused by the wind, of no particular size. Waves may be breaking, (white horses) or breaking near the shore, (surf), but the wake of a boat is not really a wave. It's the visible turbulence left behind.
A boat leaves a bow wave and a stern wave. These are not really the wake, and may well not show as a streak.
So, in British English, there is not really a "ship swell". On the west of Britain we would refer to "an Atlantic swell" indicating that the motion originated distantly, in the ocean. (In Britain, the ocean is far away. The sea is what you see from the beach.)
And, what is a ship, and what is a boat? that's probably one for a different forum.