Agreed with the above. Generally they are pretty hardy and most will grow quite fast, especially with strong light and water flow. They are usually competitive dominants and can sting and overgrow other critters. Some primarily grow upright (branches, plates, columns) while others are primarily encrusting. Even those that tend to grow upright will encrust quite a bit most of the time though.
Personally I think they are absolutely spectacular and a tank that includes Millepora (very rare) always reminds me much more of a real honest-to-goodness coral reef, which has always been my goal with reef tanks. They are great corals, but I'd STRONGLY suggest keeping them on rock islands, so as to keep them from becoming invasive.
As for what's a "coral" vs. what isn't: it depends entirely on what we decide to call something. Those animals we call corals are a hodge-podge of distantly related organisms and excludes more closely related organisms.
For example, we call hard corals "corals" and we call soft corals "corals" but we call sea anemones "sea anemones," zoanthids "zoanthids," and mushroom polyps "mushroom polyps" even though anemones, zoanthids, and mushroom polyps are relatively close relatives of stony corals and soft corals are only distant relatives. In fact, mushroom polyps group out phylogenetically in the middle of the stony corals. They are, quite literally, naked corals. We also call hydrozoans like Millepora and Stylaster "corals."
The name "coral" is applied to several groups of distantly related anthozoans, but not to other anthozoans, and to a group of hydrozoans. Phylogenetically this makes no sense in the world, but nonetheless that's what we call them.
