Formal Definitions:
Plane-a flat surface on which a straight line joining any two points on it would wholly lie.
Shape–the external form or appearance characteristic of someone or something; the outline of an area or figure.
Frame–a rigid structure that surrounds or encloses something.
My definition;
Plane– The surface that the subject is on, typically in the background supporting the main object but not what grabs your focus.
Shape– Shape is the form of the subjects in a composition.
Frame– I think frame has to do with the composition of a piece. Framing can also be what you decide to leave out of an image.