The pic is not as sharp as I'd like, but here it is. There are 2 kinds that I know of that would be called "Fire Coral".
Copied this information for you from my LFS:
The Fire Coral is actually not a coral at all, but a relative of jellyfishes and anemones. It is usually branching is often yellow-brown in color. Being that it is a relative of jellyfish, it has stinging cells called nematocysts that can deliver a powerful sting - DO NOT TOUCH! Fire coral mostly relies on symbiotic zooxanthellae for food but can also filter feed. Beware when placing near other corals, as the nematocysts can also sting them. This is the type I have.
There is a different kind called Stylaster sp., it is purple and completely different care- it is doesn't contain zooxanthellae so it needs feed. Here is some information on those too.
Copied from another source:The Stylaster Purple Stick Coral is often mistaken for a small polyp stony coral (SPS) because of its hard purple exoskeleton, when in fact, it is classified as a Hydrocoral. Unlike Fire Corals, which are also Hydrocorals, most species will not sting other corals in the reef aquarium. It is commonly referred to as Lace, Ember, or simply Stylaster Coral. Its body is made up of calcium carbonate, and its beautiful, lacy, fan-shaped branches with blunt tips are very fragile. Its tiny, clear polyps will extend from the grooves along its fan-like branches.
The Stylaster Purple Stick Coral is peaceful towards other corals in the reef aquarium. It should only be added to well-established tanks. Provide low lighting and a medium to strong water current in the aquarium, along with the addition of calcium, iodine, strontium, and other trace elements to the water. Placement under overhangs will provide a good environment.
It does not contain the symbiotic algae zooxanthellae, and is dependent on regular feedings of supplemental foods such as micro-plankton.
Hope this helps some.
Matt