You’re thinking of sea lampreys. Remoras don’t do any damage and just hitch a ride.
Actually, remoras have a suction of around 30 lbs. per square inch. I really didn’t want the sensation of the one attacking me. Imagine the bruise! And I’d have a really hard time explaining it my husband.
Yes, a remora did attack me for about 15 minutes. It was hand-to-fin combat! My dive buddy was no help except that he nearly choked himself to death laughing so daddgum hard.