There are a number of questions here on Stack Exchange discussing the distinction between organic and inorganic compounds, such as:
The distinction between organic and inorganic chemistry is one that is upheld mainly because of traditional reasons. It is also upheld because some more specialised fields are often well included into one of the two traditional definitions: solid state chemistry is usually inorganic while natural product synthesis is almost entirely organic chemistry by all applicable definitions (save the very old historical ones).
But remember that there are a number of fields that straddle the boundary. Coordination chemistry often involves organic and inorganic ligands around an inorganic metal centre. It depends on the research being performed whether the group wishes to be considered organic or inorganic. See for example the groups of Professor Klüfers and Professor Knochel at the LMU Munich: The former classifies himself as an inorganic chemist and investigates carbohydrate-metal complexes among other things; the latter classifies himself as an organic chemist and investigates organometallic reagents and reactions.
So in a way, the organic/inorganic distinction compares well to the border between Europe and Asia. Everyone will agree that France is in Europe and China is in Asia but what about Georgia and Turkey?
Note that your dualism is short-handed. $\ce{SiHCl3}$, trichlorosilane or silicochloroform is produced in an industrial scale and trichlorogermane $\ce{GeHCl3}$ is also known. On the silicon side of things, apart from tri- and tetrachlorosilane the di- and monochlorosilanes $\ce{SiH2Cl2}$ and $\ce{SiH3Cl}$ are known just like their carbon counterparts. And of course, silane $\ce{SiH4}$ is known, too. (I am not sure exactly how much is known about the corresponding germanium compounds. The English Wikipedia didn’t have entries for them but didn’t contain trichlorogermane either, which was only present in German and Russian.)
So beware when drawing analogies. They could go into a different direction that you may think.
Speaking of surprising facts: Did you know that chloromethane is the most-produced secondary metabolite by mass? So let’s add chlorosilane into the organic realm by analogy!
Finally, as an aside note: I actually use tetrachloromethane much more than I would carbon tetrachloride; that goes for both languages in which I do chemistry.