What material is the seat of your pants touching?
If it is touching wood, the chair is not upholstered.
If it is touching cloth, leather, or similar material, the chair is upholstered.
In an automobile, the seats are always upholstered.
An office chair in which the seat can turn or pivot is "a swivel chair." A swivel chair may or may not have wheels. The wheels are often called "casters." Nowadays a swivel chair would usually be upholstered, but I have seen (very comfortable!) wooden swivel chairs that were not upholstered.
An "easy chair" is an upholstered armchair that is thickly padded.
All of the fabric and padding on a chair are the "upholstery." When it wears out, you might send the chair out and have it "reupholstered."