An antiperspirant, usually applied to the armpits, retards sweating.
A deodorant interferes with bacterial action on sweat or other bodily fluids to retard odors. Deodorants are often applied to armpits, feet and other body parts that may be subject to unpleasant odors.
Body spray is a (usually weaker) aerosol deodorant that can be sprayed anywhere on the body.
Perfume/parfum, toilette and cologne are all scents (in descending order of concentration) designed to give the user a pleasant odor. They do nothing to prevent unpleasant odors, except perhaps to cover them.
P.S. None of the above preparations works particularly well unless one has bathed/showered with soap and water beforehand.