To a scientist, they're a hobby classification - they don't split stony corals like that.
In the hobby, there is a general splitting based on polyp size. There are problems with it [as there's no biological splitting point] and in general IME stony corals of all sorts prefer generally the same conditions ... but the definition above will get you a handle on how reef boards/etc split these corals into two.
Many various specimens may fall into either or category depending upon who you ask. Some like galaxia's have a "medium" sized polyps when compared to acropora's and frogspawns. So it may be listed as an SPS or LPS from time to time, along with many other medium sized polyped stoney corals.