Well, I guess I should clear up what I said. Seamoths *used* to be classified with seahorses. With the advent of phylogenetics, they have since been reclassified.
Seahorses:
Order Syngnathiformes
Family Syngnathidae
Seamoths:
order Gasterosteiformes
Family Pegasidae
So, by current standards, they are about as closely related to seahorses and relatives as clownfish are. If anything, they are more related to the brackish sticklebacks than seahorses.