In general, the easiest way to tell that bubble corals and frogspawn/anchor/hammer corals aren't soft corals is by the fact that they all have a hard skeleton that the soft bits grow around.
Soft corals are members of the octocorallia - they have tentacles that grow in groups of eight. Stony corals (SPS and LPS) are hexacorallia - they have tentacles that grow in groups of six.
Just to confuse things, there are two members of the octocorallia that have stony skeletons - blue coral (heliopora) and organ pipe coral (tubipora). They're still normally considered soft corals.
More exceptions and qualifiers: Gorgonians are also octocorallians, so in a sense they're soft corals, too. Although many people include zoanthids and mushrooms (corallimorphs) as "soft corals", they're actually hexacorallians.
Soft corals include finger leather, christmas tree, devils hand, cabbage leather, toadstool, xenia, anthelia, "blue xenia" (actually cespitularia), Kenya tree, colt, carnation, spaghetti leather, cauliflower leather, green star polyps, clove polyps, etc.