3D printing, or additive manufacturing, is the process of building parts by joining material layer by layer from a CAD file. This is unlike a traditional manufacturing process, like CNC machining, where a part is built by subtracting material from a block of material. 3D printing and additive manufacturing can be used regardless of whether the parts are fabricated in plastic, metal, or rubber.
Rapid prototyping is the technique of fabricating a prototype model from a CAD file. In other words, 3D printing/additive manufacturing is the process and rapid prototyping is the end result. Rapid prototyping is also used to describe any prototype parts that are needed ASAP, including urethane casting, injection molding, and CNC machining. 3D printing is just one of many applications under the rapid prototyping umbrella.