They both make you smell great, so aren't they essentially doing the same job?
Well, no. Body sprays are a lot like perfumes - containing fragrance extracts such as herbs, oils and spices, mixed with alcohol and water.
So they can help you smell great, giving you a fresh scent that lasts for a few hours. But they don't stop you sweating. In effect, they're only masking body odours, rather than stopping them.
OK, so you may have a favourite body spray that has you signature smell. No problem, just use an anti-perspirant deodorant as well.
That way you can be confident you're protected against wetness and odour, and still smell of your favourite scent.