Sateen is a special type of weave using 100% cotton yarns. By weaving the cotton with four threads over one thread (as opposed to a standard one over, one under), the resulting fabric is super soft and with one side that features an illustrious shine.
Satin, on the other hand, is most often used to refer to a polyester fabric that features a highly slippery surface, mimicking the look of silk. Think the satin jacket of the 1970s or satin sheets from the Disco Era.
Though they can sometimes have a similar appearance, since Sateen uses 100% cotton yarn, the end result is a textile that is much more breathable and durable than its Satin counterpart.