You can take the same cotton yarn, weave it in four different ways and end up with four completely different fabrics. The difference lies in how the threads pass over and under each other.
Renforcé is the most classic plain weave: one thread over, one thread under. It is woven fairly loosely from relatively thick yarn. It is durable and economical, and lasts for years in a child's room. Percale is also a plain weave, but with finer yarn and a much tighter construction. It looks matt and feels slightly crisp and cool to the touch. Poplin, with fine crosswise ribs that come from a slightly thicker weft, is a close relative of percale.
Sateen is another world. Here a thread floats over four threads before passing under one. These floats reflect light; that is where the sheen and the smoothness come from. There is a price: long floats are more prone to snagging and wear over time. A practical rule: someone who sweats at night and sleeps hot will be comfortable in percale. Someone who feels the cold and wants to be wrapped up when getting into bed will love sateen.