[Van down by the river]

The First item is Psammocora contigua This coral is often overlooked by hobbyists as it often arrives brown. I've had many of these turn emerald green or brick red after settling into the reef. Cat's paw refers to numerous species.

As to the second one I'd say maybe Hydnophora exesa

but more likely: Pavona explanulata
Can you get a closer picture of the polyp structure?