First one looks like a flower pot or daisy coral to me. (goniopora)
Something the lines of
http://www.freshmarine.com/flower-pot-coral.html
http://www.arkive.org/flowerpot-corals/goniopora-spp/
Edit: These have a low survival rate in a new tank.. It can be done but its not easy.
The 2nd one looks like a Birds Nest SPS.