There are lots of coral groupings. You can be scientific about it and look at coral classification and see what order, family, and genera each coral group falls into or you can use the common coral groupings that hobbyists collectively created.
Three Basic Groups of Corals Terminology used in this hobby: Soft Corals, LPS, SPS.
Soft Corals
-Lack a skeleton. They're squishy. You could literally squish them into nothing.
Example: Zoa (Zoanthid)
- Each of those circular openings is a polyp. At the very middle of each 1 is a small opening where the mouth is.
- The second picture shows two of the polyps closed up. We just fed them some food, their feeding response was to close up.
- What makes these a soft coral is they lack skeleton. Zoas grow by extending and attaching their flesh onto a substrate for attachment and new polyp development.
Large Polyp Stony (LPS)
-Corals possessing a hard skeleton with large polyps.
Example: Acan (Acanthastrea)
- See how it's just one large polyp? Underneath this flesh there is a skeleton which the flesh can retreat into.
- You can even see the mouth at the very middle of the polyp. Looks like a pair of blue lips.
Small Polyp Stony (SPS)
-Corals possessing a hard skeleton with several small polyps.
- This is an acropora. See the red circle in the picture? That is 1 single polyp. They're much smaller than the polyp of a zoanthid or an acan.
- There are probably several hundred polyps on this acropora colony.
These are just some examples of the corals in each category but that pretty much sums it up. Any questions feel free to post more questions. Lots of helpful people here on reef2reef.
In taxonomy, the terms "LPS" and "SPS" isn't even used. Stony corals all fall under the Order Scleractinia. While what we consider soft corals (anemones, zoanthids, corallimorphs) are all under their own different orders.