Self-directed play is where the child isn't playing according to "rules". Where there's no "right" or "wrong" way to play, and the child is making up their own game/world/etc as they go. Think "Lego" :)

Self-directed play is simply kids playing on their own terms, making up games with their own rules, making up their own characters etc. You know.. being a Kid and playing with your imagination.

Play directed by the child, ie, the child sees a book next to a soft toy and chooses to look at the book, rather than being directed by a video saying "let's read a story now".