Plastic wrap and cling foil are the same. The most popular brand of plastic wrap in the United States is "Saran" wrap. In the US, we use the terminology of "aluminum foil" but "plastic wrap."
In other countries, plastic wrap may be referred to as cling foil. It does come on a "foil" roll, and it clings.
In regards to hair, plastic wrap/cling foil can be used to complete a "silk wrap" hairstyle. A Silk wrap is when hair is dry wrapped around the head with a lightweight silicone based serum and sealed with the plastic wrap, cling foil, processing cap, or "hydracap" for up to 10 minutes under a platform dryer set for medium heat. (You do not want to sweat.) The desired result is shiny hair with movement.