There is a difference that I think is best summed up by Robert Lane as seen on the Elements of Visual Design website:
Composition is the manner pieces or components are combined and arranged visually to tell a story. Proper composition considers alignment, grouping, placement, space, and visual flow within a layout. This layout can be any medium. Once a proper audience and purpose have been determined then composition, components, and concept can encompass that identified purpose allowing a successful design.
In other words, Composition can be seen as the elements that make up the design:
Composition
• the nature of something's ingredients or constituents; the way in which a whole or mixture is made up.
Whereas layout is the organization of said elements:
Layout
• the way in which the parts of something are arranged or laid out.