They are. They are all pomacentrids (family pomacentridae). Clowns are separated by some into the subfamily amphiprioninae. Others don't recognize that level of separation.
To give another example of what a family means, humans, gorillas, chimps, orangs and australopithecines are (or were) all in the same family, hominidae.
So, the point I am trying to make is that lumping clowns with damsels is like saying people and orangs are similar. Same basic body plan, but I wouldn't let my sister date one.