No, I didn't. I described two types of deodorant product.
One type attempts to neutralise a smell, usually by targeting bacteria. This doesn't have a name other than "deodorant" - For example, this is how crystal deodorant works. It won't prevent you from sweating, it just tries to stop the sweat from smelling bad.
The other type tries to block sweat, this is an "antiperspirant" or "antiperspirant deodorant".
I'm not sure whether there are types which do both - probably.
Something that just adds a smell without neutralising smell or blocking sweat is not a deodorant. You wouldn't call a perfume deodorant. Body spray is essentially a very weak perfume.
Maybe OP doesn't need deodorant - not everyone does. (I definitely do!)
BO is caused when you sweat and the sweat contains bacteria which produce the BO smell. It gets worse the more sweat there is, the longer you leave the sweat before washing it off, and if there is dirt/dead skin in your armpits for the bacteria to feed on. Also, if sweat bacteria soaks into your clothes, they aren't always removed by washing at 30-40 degrees, so it can make the clothing smell when your body heat warms them up.
If you don't sweat very much, and your sweat doesn't have much of the smelly bacteria, then fresh sweat on clean skin might not make much if any smell and so you might be able to keep on top of it just by washing your armpits and your clothing regularly, and not need deodorant. Therefore body spray is fine.
For most people though, washing is not enough. Either they have smellier sweat due to diet/hormones/random genetics, or they are very active and produce more sweat, or their normal sweat amount during the day is enough that you'll notice a smell before the end of the day.