I think that first coral is some weird Montipora too.
#2 has growong tips that looks more like Stylophora/cat's paw etc look with the super smooth rounded growing tips. Montipora is a bit more jagged (picture those growing tips on a standard Monti d = they remind me of those)
I think if a pic with the polyps out was available, that would clinch it.
edit: dansin, you have to look much more closely at the detail of stony corals if you think those two pics are the same coral.
look and compare: the growing tips, the branching structure, the like raised veins/ridges on the base of #1, the color of the growing tips, the pattern of the polyps(too bad we can't see #1) and so on.