No, they are different compounds, although both may be used cosmetics.
Polysorbate 20 - Polysorbate 20 is commonly used to emulsify oils and water at a 1:1 ratio. It is a nonionic surfactant that is water-soluble and used as a dispersing agent. It is gentle and nonirritating. Normally, you need a solubilizer, such as Polysorbate 20, to mix your essential or fragrance oils into body sprays without separating. Combine equal amounts of your fragrance or essential oil and the Polysorbate 20 until you achieve a clear solution, then, add this mixture to your water or alcohol. It is a polysorbate-type nonionic surfactant formed by the ethoxylation of sorbitan before the addition of lauric acid. Its stability and relative nontoxicity allows it to be used as a detergent and emulsifier in a number of domestic, scientific, and pharmacological applications. As the name implies the ethoxylation process leaves the molecule with 20 repeat units of polyethylene glycol.
Palm oil is obtained from the fruit of the oil palm tree. As food, palm oil is used for frying. Industrially, palm oil is used for manufacturing cosmetics, soaps, toothpaste, waxes, lubricants, and ink. Palm oil contains saturated and unsaturated fats, vitamin E, and beta-carotene.
Some people and organizations discourage the use of Palm Oil due to the ecological impact of getting it in Africa. An alternative could be coconut oil, which is a cultivated and exported crop from most parts of Asia.