I agree that the first is Hydnophora. Make sure to keep it far away from any other corals. For an SPS, they have remarkably long tentacles and will literally EAT anything that they can touch. I've not seen any other coral that can stand up to it's abuse. I've had branching and encrusting Hydnophora and they grow very quickly and don't require near as much light as most SPS. I've seen mine produce 2" sweeper tentacles.
The second coral is a mystery, other than Acropora.