paddle board

Paddle refers to the rider's arm action, the same as paddling a surfboard, not to a separate physical paddle (no such paddle is used with this type of board).

paddle board (plural paddle boards)

1. A large fat board used for surf lifesaving. It is propelled by the rider using their arms, either lying face down or sitting up on their knees, and usually has straps positioned along the sides to hold onto.
   • 1997, 17 October, Simone Cotter on ABC Radio National, Surf Lifesaving [1]

     you'd probably grab a paddle board and paddle out and grab them, instead of swimming out