Fauteuil large chairs, upholstered, with substantial arms, the kind of chairs you would put in your salon or living room.
So, les fauteils are a subset of les chaises. "Chair", being a much more general term, is a very poor translation of fauteil. In my opinion, it should not be accepted.
"Armchair", however, looks to be identical to fauteil.
Some images of fauteil: