Polysorbates are ethoxylates of fatty acids esterified with anhydrosorbitol. Polysorbate 20 is a polyoxyethylene derivative of sorbitan monolaurate whereas polysorbate 80 is a polyoxyethylene derivative of sorbitan and oleic acid. And as much as I love chemistry, I realize this really isn't all that helpful...
Polysorbates are emulsifiers, wetting agents, and solubilizers that we use to bring small amounts of fragrance, essential, or carrier oils into a watery environment. We can use them to emulsify an all oil ingredient in our bath, or to make a water based product with a tiny bit of oils in them.
One difference between the two is their HLB value - polysorbate 20 has an HLB value of about 16.7, whereas polysorbate 80 has an HLB value of about 15. (Click here for a list of HLB values!)
The other difference happens in our products. We generally use polysorbate 20 to emulsify fragrance or essential oils in water, whereas we generally use polysorbate 80 to emulsify carrier or more complicated oils in water. If I were to make a shampoo to which I wanted to add 2% fragrance oils, I'd use polysorbate 20. If I were to make a shampoo to which I wanted to add 2% olive oil, I'd use polysorbate 80. If I were to make a bath bomb or bath oil, I'd want to use polysorbate 80 to carry the heavier oils into the bath water and make them disperse.
That's the long answer. The short answer is that we use polysorbate 20 to emulsify small amounts of lighter oils and polysorbate 80 to emulsify slighter larger amounts of heavier oils.