they aren't. Ceramics (and by relation, ceramite) are defined as "inorganic, non-metallic solids." Anything with Carbon in it is technically organic.
What are you talking about? Diamonds are hardly organic. Neither is graphite, or other forms of carbon as such.
Organic chemistry deals with substances that form around carbon chains, but that doesn't mean that carbon itself would be any more organic than, say, sulphur or silicon. In addition organic compounds pretty much always also have hydrogen in them, and oxygen and other stuff in the more complex ones.
Also, ceramite to me sounds like technobabble and we can only guess based on etymological reasons that it might be related to ceramics as we know them, but we don't really know for sure. It's all circumstantial evidence. For all we know it could indeed be single-molecule slabs of carbon nanotube or whatever.
Can you even make any connection between the terms of sci-fi tech and current terms that resemble them? Take the Dune/Star Wars "
plasteel" for example, Is it plastic or steel? Steel that has plastic qualities? Plastic as durable as steel? And is "
transparisteel" just transparent steel or some transparent substance that has material characteristics comparable to or better than steel?

Transparisteel was a hard and completely transparent metal alloy. This made it a commonly used material for starship viewports, and the windows of strongholds, and other buildings where security was a must. In starship viewports, transparisteel could be made photosensitive to become more opaque near bright explosions, while traveling through hyperspace, and such. A major component in the make-up of transparisteel was lommite.
Transparisteel was marginally less strong than its opaque counterpart durasteel.
Okay, technobabble checks out... except that
transparent metal doesn't exist. The free electrons in any metallic substance tend to make it quite opaque, and that by definition is caused by the nature of metallic bonds so clearly transparisteel is not metal
as we understand metal.
Similarly, ceramite might not have anything to do with ceramics as we know the term.