I snorkel the Florida Keys a lot and there are a lot of gorgonians. Near shore in shallow flats they are mostly photosynthetic varieties. But the purple, non-photosynthetic version is common there as well. We also have them in the Gulf of Mexico along the SW coast of Florida where I live.
Out on the big reefs (most are a few miles off to the southeast of the Keys) there are a lot of non-photosynthetic gorgonians that are commonly called sea fans. They are 100% protected and the fines for taking one are substantial. I can't say I,ve seen any other non-photosynthetic gorgonians in the Keys. But then I don't dive, I snorkel, and seeing smaller non-photosynthetic gorgonians may just be beyond my vision abilities.
My best guess is that those may be less purple than they look in the photo and that they are photosynthetic. The purple gorgonian that is NOT photosynthetic is a skinny main stalk some have vertical ribs or ridges that run up and down and some don't (they are 2 different species). The polyps are white. They like higher flow and every so often, maybe once every month or two, they shed the outer layer of purple to get rid of any algae that may have attached to it.
As for keeping the purple, non-photosynthetic gorgonian, I've had some short term luck, like a year or 2, but never long term. I've had better luck with the other NPS gorgonians that are yellow and red which I've had long term, just like most other corals. But I do spot feed, I tend to feed heavy and I shut off all pumps for 10 to 15 minutes when I feed, then fire up just internal flow for a minute to get things stirred up again and then back off for 10 more minutes and more spot feeding. The photosynthetic gorgonians are easy. I'm developing a 75g hexagon tank to keep 4 to 6 species of gorgonians so I can try and keep a few Flamingo Tongue snails that only eat gorgonians.
Here is a purple gorgonian that washed up on a SW Florida beach during a storm attached to a clam. It is still alive in my tank, but it does struggle.
Here is a close up of it in my tank.