Are all non aromatic carbon chain aliphatic ?
Incorrect. Read the first sentence of the first link you posted:No, or as best I can understand, I believe no. One kind is distinct from the other kind. Review this classification from your textbook. For alternative review or maybe reenforcement, you might look at these two articles.
I understood this stuff better, but a very very long time ago.
Correct."Carbon chain" seems a bit inprecise. If one rephrases the question to "Are all non aromatic hydrocarbons aliphatic ?" I recall the answer is yes by definition of basic classifications?
Fine. It makes better sense. A careful re-reading was needed.