There are mushrooms (which are corallimorphs), these are squishy and related to anemones rather than corals but still considered corals for simplicity. They are easy to care for and great beginner corals, often hitchhiking on LR.
Mushroon corals of the family Fungiidae are true stony corals that come in a variety of shapes and sizes with the most common being fungia, cycloseris, and herpolitha. These are harder to care for but not explicitly expert corals. Although fairly common withing their distributed range they are rarely encountered as hitchhikers