Maybe this will help clarify a bit:
Moissanite = all crystals formed using Silicon and Carbon (200+ sub-types). Generically tends to refer to naturally formed crystals, in honour of Dr. Henry Moissan who discovered it in the meteorite.
Silicon Carbide = also refers to all crystals formed using Silicon and Carbon (200+ sub-types). Tends to refer more to the lab grown and is the preferred 'scientific' term. You will not find semiconductor papers referring to any of these crystals as "moissanite" for example.
You can see, that we have 2 generic family names, for a family of over 200+ crystals that all share one feature - namely being composed of silicon and carbon.
As noted, C&C took a specific form of Moissanite / Silicon Carbide and named it "Moissanite by C&C".
The Amora Gem, by BTD, is a different form of Silicon Carbide...in other words, a different type of crystal than "moissanite by C&C", but still a member of the 200+ Silicon Carbide family.
So, two differing crystal types, but both fall within the domain of being termed either Moissanite or preferably, Silicon Carbide.
You can thus see how C&C basically took one title of the family's last name and basically used it as a first name, which has thus created confusion.
If they had called their crystal ABC gem, and we called our's the Amora Gem, then there would not be so much confusion