The important thing is that the referent of the term describing the unusual feature of the engine defaults to "cylinders" (or equivalent). So for example an engine with 2 camshafts is a "twin cam", while an engine with 2 cylinders is just a "twin". (Of course you can call it a "twin cylinder" if you want to, and people will still know what you mean, but if you do it the other way round and call a "twin cam" engine just a "twin", they won't.)
So, with a shuriken-shaped engine with a fixed block, the unusual feature is that the cylinders are arranged radially to the crank axis, so it is a "radial engine". (You can also have a cylindrical engine with cylinders parallel to the crank axis, which is an "axial engine".)
With a shuriken-shaped engine where the crank is fixed and the block goes round, the unusual feature is that the cylinders rotate, so it is a "rotary engine". (The same default-referent thing applies: the radial cylinder arrangement is the default for this sort of engine, so you don't have to say "rotary radial engine". But you might have to say "rotary axial engine" if you were talking about one of them.)
With a Wankel or any of the zillion variants on the theme, the unusual feature is that the piston goes round, so it is a "rotary-piston engine". The piston isn't the default referent (ie. cylinder or equivalent), so you have to specify it. People often don't, because they are lazy and don't care about being confusing, but that is a silly way to talk.
You could, if you really wanted to, make an engine where the piston goes round and the "cylinder" is parallel to the crank axis, and have a "rotary-piston axial engine". It would probably be shit though. You could also make it with the crank fixed and the block rotating, and have a "rotary-piston rotary axial engine", but that would not make it any less shit.