There are two basic types of hard (or stony) corals: LPS, or large polyped stony, and SPS, or small polyped stony. The distinction between LPS and SPS is a hobbyist thing, and biologists do not divide corals this way.
In general, you will probably have better luck trying to keep LPS with soft corals. SPS and soft corals do not typically get along well. Note the "probably" and "typically" above, because there are always exceptions.
LPS include bubble, frogspawn, duncanopsammia (often called duncans), donut, meat, etc. SPS are the "colored sticks" (and sometimes plates), like acropora, montipora, etc.
As mentioned previously, the catch when keeping LPS with soft corals is that both sides have potent defenses. Soft corals produce chemical warfare agents to damage and stunt the growth of other corals. LPS tend to have "sweeper" tentacles that extend much further than you'd expect, and often contain enough nematocysts to kill soft corals.
Running carbon can help to remove soft coral chemicals, but only distance will protect corals from sweeper tentacles.