Not really sure what you mean, but I'll try to explain it.
First of, the common classifications (softies, LPS, SPS) aren't true scientific classifications. They're just more for hobbyists to generalize coral needs. Polyps are each individual organisms that live in a colony or singularly.
If you're coming from soft corals (mushrooms, zoanthids, etc), then a mushroom is a "polyp", a single zoanthid is a "polyp", etc. These corals don't build a skeleton...instead they are made up of little calcium-based splinters that help support their weight. You may have noticed that in the center of each "polyp" is a mouth that can eat food.
SPS are "small polyped", and build skeletons.
LPS are "large polyped" in most cases, but there are some corals that blur the SPS/LPS line. Just like all other polyps, these too have mouths to eat and tentacles to catch food with. However, LPS are more likely to live singularly than SPS/softies (can't even think of an example for SPS.) In the case of "brain corals", they are often just one HUGE polyp (sometimes with multiple mouths.)
Here's an Acanthastrea coral of mine. Each individual main circle is a polyp. The inner circle is where tentacles come out, and the center of each polyp is the mouth.
Hope that helps!