Perfume = not just perfume/cologne that people wear just for the scent, but also the scents added to most hand and body soap, shampoo, conditioner, deodorant, aftershave, shaving lotion, hair spray/gel, laundry detergent, fabric softener, dish soap, household cleaners, hand sanitizer, moisturizing lotion, and air freshener. (Basically all the "fragrance" and "parfum" that's put in personal care, beauty, hygeine, and cleaning products.)
Body odor = armpit stink or how people smell after a lot of physical exertion or when they haven't washed for a good while (rather than just the unique-to-the-person smell that someone has all the time, even right after a shower).
I find it easier to tolerate body odor. There are exceptions (mostly ... maybe entirely ... because of the odd perfume-y scent that I actually like or find neutral), but generally I would rather everyone smelled like body odor than perfume. I don't like the smell of body odor, I just don't find it as horrible as the majority of perfumes.
I find that perfume doesn't even cover up body odor, so people will just smell like a combination of their body odor mixed with whatever perfume(s) they're wearing; Which, depending on the particular body odor and the particular perfume, can be far worse than even a really awful perfume alone.
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