I have a feeling my answer will change over time but for now…
Motion graphics the result of motion design.
Motion graphics are the end product, they are what you see, hear and experience.
Defining Motion graphic design is more complex than purely calling it graphic design in motion. It may well be constantly evolving. It is a combination of technology, graphic design and, communication, it is the process of visual communication and creative problem solving, using colour, space, image, sound in time. Utilizing essentially whatever techniques are available in image making, and audio design in order to fulfil a specific brief, communicate a message or idea. There is purpose, possibly a commercial one.
As motion designers we are able to utilise more and more techniques. With the help of new technology that is more simple/ easier to use, cheaper to produce effects seen in Hollywood blockbusters, we can dip in to all this, should they help in creatively solving the problem. Where technology keeps changing motion designers may well be able to benefit from newer techniques. Projection mapping, interactivity, 3d stereoscopic techniques, while now are highly cutting edge and expensive, could become more commonplace. In which case I would see it that motion design will always be at discipline that is at the cutting edge of image making.