Usually not a different board, but a slightly bigger one. Fresh water is less dense than the sea, so the same board floats about 3 percent lower; and a pool wave is the same every time, which rewards a board you already know.
Sea water is about 2.5 percent denser than fresh. On a 35-liter board that is roughly one liter of float gone, enough to feel on a paddle-heavy day. The calculator has a water type input that adds it back into the number.
In pools that produce a mechanical, peeling wave, most surfers ride their everyday shortboard or fish with a liter or two extra, because the take-off is late and the wave is not powerful. For a first pool session, the board you catch the most waves on at the beach is the right one. Beginner sessions put you on the pool's own soft-tops.
More guides: Beginner board size · Soft-top or hard board · How many liters is too many · Foamie to fiberglass.