They are probably one of the easiest soft corals to find although getting a nice assortment is not the case. Purple and reddish ones are widely available. Other types are not.
Mushroom corals are soft corals and have no exoskeleton but grow on rock.
The rock does not need to be flat, it can be shaped in just about any form. The cap can be real round or somewhat ruffled depending on the type. Generally the stem is short and not all that visible. The corals can be mono colored or multicolored, can be smooth or rough, with knobs or stripes running across the cap from the inside towards the exterior. Mushroom corals are generally considered hardy but that does not mean that they take abuse real well.