Is an arene the same as an aromatic compound?
Almost, arenes are aromatic hydrocarbons, compounds that typically contain benzene rings.
The designation 'aromatic' and 'aliphatic' refers to compounds which have benzene rings, and which do not have benzene rings, respectively. These are older terms, which stem back to an early (incorrect) theory that it was benzene rings which gave rise to a sweet odour in organic compounds.
To be a little more precise, aromatic compounds are conjugated planar ring structures, and can include compounds such as pyridine which have five carbons and a nitrogen in the ring.
So, Arenes would be a subset of Aromatics - those which are also hydrocarbons.