Aliphatic compounds could be straight chain structures [Acyclic] like alkanes or cyclic structures, like cycloalkanes.
Aliphatic compounds are hydrocarbon chains - strings of carbon atoms connected to each other with hydrogen atoms hanging off the sides of the chain.
one exception for the definition of aliphatic side chain is Proline which also has aliphatic side chain but the its side chain is bonded to both carbon and nitrogen.
Aromatic compounds have benzene ring (older notion). Aromatic compounds are those which follow Huckel's rule. (4n + 2pi) rule. They have the general formula: CnH2n-6 [where n is equal to or greater than 6]
Aromatic compounds are rings - so take the chain and connect the two ends together to form a continuous loop.