Shots in the dark based off the pics would be..
Caulerpa 1 = a form of Caulerpa racemosa, potentially C. peltata or C. nummularia, both of which show the little 'ball's of the algae (which are characteristic for racemosa) as flattened little mushroom like features.
Caulerpa 2 = looks like very similar to C. sertularoides, or saw tooth Caulerpa. The fronds look short and stubby, though its too hard to get to a better level than that. They also look to be about the right size for this particular species.
Better photos (Frick-n-Frags' suggestion is awesome!) would assist greatly.
Overall.. are you trying to see if they are desirable? Or aiming for a battle strategy on how to eradicate it from the display?
Very few people who enjoy keeping their reef aquariums as reefs allow Caulerpa to infest the main display. It can work as a refugium algae, but its rapid, aggressive growth rates make it a nuisance in most aquarists' displays.
>Sarah