There is article of S. P. Cairns about
Dendrophylliidae , that includes sun corals (
Tubastrea, globular not branching, except the black ones) and their cousins (branching or not Dendrophyllia, Cladopsammia, and other less common corals.
Tubastreas (intense orange, pale pinkish-orange and yellow, all not branching) are most common, compact branching black Tubastrea diaphana is also frequently available, and Tubastrea micrantha (long branching, lighter shade with greenish tentacles) is rare and -as I had read, don't have it - requires higher flow and daily feedings.
Dendrophyllias are usually more expensive, than Tubastreas, and if not - more rare. Some of them are open all day long, when Tubastreas and Cladopsammia gracilis are predominantly nocturnal. But basic care is the same.
You can see photos in
this thread,
this, and
this. The last site shows uncommon for us varieties too.
I have what I think is T. faulknery (pale pinkish-orange), T. coccinea (deep orange), T. aurea (lemon yellow, high polyps' skeletons), the same, only branching (possibly Dendrophyllia cornigera), T. diaphana (compact branching black) and Cladopsammia gracilis (low growing bush shape, smaller diameter of polyps).
If colonies are not starved too much, with recessed tissue, then care and feeding is the same, with no particular sensitivities. All are mostly nocturnal, but open for a feeding during the daytime too.
It the starved colony not opens at once for a feeding, then making it open efforts will be required. Easier to buy well fed plump colony.
Black starved Tubastrea was very slow in opening to feed, up to 1.5 hrs each session, pure yellow starved Tubastrea was closing, as soon as flow was off for a feeding. Others opened at once, independently from their condition.
I would say that they are more or less the same, except, as I had read, T. micrantha.
HTH