This is a question of semantics rather than finance. Within the context of the Royal Navy, a ship being "paid off" refers to it being removed from the order of battle and returned to port, usually as a prelude to being fully decommissioned. As a turn of phrase, it dates back to before the professionalisation of the Royal Navy started by Robert Blake following the Anglo-Dutch Wars: officers and crews often signed their ships on to the fleet for a specific period, crisis or expedition, and upon completion would return to port and be 'paid off' and return to civilian life. This created a problem when the government would try to keep ships and crews at sea as long as possible to avoid paying them the back-pay they were due, which created significant issues with both the morale of the crews and the maintenance of the ships themselves, so while the practice was discontinued, the phrasing remains.

I'd recommend N.A.M. Rodger's The Command of the Ocean for an excellent and detailed look at the development of the Royal Navy as a professional fighting force.