Ok, I found some photos.
First off, I wanted to comment about the feather caulerpa. One variety of it is actually banned from introduction in California waters. I think it is called Caulerpa taxifora, or Caulerpa prolifera. It has a feather blade. You will see signs along the beach and posted at many of the aquariums, warning people about the invasion of this caulerpa in the ocean. It has been introduced accidentally and has caused dameage to the ecosystem in that region because if its rapid growth.
Of course it is fine in the aquarium, but it is a rapid grower and and be kept to the refugium and not placed in the main display with LR and corals.
In my experience, the cheato, prolifera, and mexiacana varieties are rapid growers. The others grow slower and are more beautiful.
Here are a few varietes I collected in the past.
Razor Caulerpa serrulata
This is a slow growing, very cool looking caulerpa
Another pic of razor
Caulerpa mexicana
And then comes my absolute favorite, the grape Caulerpa racemosa. This one grows in a true grape cluster off the rhizoid (stalk). The other variety of grape caulerpa only produces semi-flat grapes that look more like a gecko foot than grapes, to me.
This last variety is of unknown species. I always called it a teacup caulerpa. It is very cool to look at and I consider it a medium grower. It was the only caulerpa that my fish would munch on, because it was softer and more delicate.
Cheers