No real difference, as you suspect. Design weight = design
displacement. Dry weight = dry displacement. On real ships,
of course, attention is paid to salinity/density of water,
which influences draft, buoyancy, etc.

But shipbuilding has been around a long time and I wonder if
a boat's weight was once measured by the actual displacement
of water in dry dock. Did ship builders years ago really
weigh ships? Would it have been worth the trouble? Did the
process of building models, measuring actual displacement of
the model, and scaling turn out to be "better" than scaling
a ship's weight from the model? Probably.

Today, of course, almost any marina can tell you what a lift
gauge reads, FWIW.