Rapid Prototyping is the technical term and 3D printing is the colloquial term for additive manufacturing technology. 3D Printing is used so that many people can grasp this technology easily. A not so accurate yet commonly perceived difference between Rapid Prototyping and 3D printing is that Rapid Prototyping is industrial level and 3D printing is consumer level additive manufacturing technology.
3D printing is a simple version of rapid prototyping technology. It costs much less and it is much more capable and versatile when compared to rapid prototyping machines. Rapid Prototyping is being used by industries such as automotive and aircraft for years. In general, 3D printers are considered much more compact and easier to operate than rapid prototyping machines. These printers are also perfect to use in office and these printers consume much less energy.
Drawback of 3D printers is that these printers are less accurate. Also the material choices are highly limited at the moment. But going forward, this is bound to change.
Please note that the difference stated above is general perceived difference. In actual terms, both rapid prototyping and 3D printing mean the same. In fact, rapid prototyping is the actual term and 3D printing is the most commonly used term.