I am really confused between the meaning of motion graphics and compositing. Is motion graphics mean using still image to create illusion of moving object and compositing is combining 2 or more clips together in the same frame?
Motion graphics consists of Graphic Design and Animation. Main focus is to deal with images, typography, color and illustrations, also it's key to work with design assets, like flow charts, icons, images or backdrops, which created with animation in mind.
However Compositing consists of Animation, Mathematics and Rating Pictures (eyeballing). Main focus is digital image manipulation - it's the art and science to combine (matching) images from multiple sources like film, photographs or 3d renderings into new (blended) images to create a perfect illusion.
Composition involves layering of multiple provided elements, such as live action footage, matte paintings, and special effects. Skills include keying, color correction, and integration. Compositing is often seamless and invisible, with the intent of making the shot appear to have been captured entirely in camera. All special effects in movies for instance have compositing as a final step to integrate the work of the other disciplines.
Motion graphics on the other hand is an extension of graphic design, but animated. The purpose of motion graphics is to tell a story, sell a product, or add visual interest. It does not produce a seamless photo-real image.
In addition to what @poor said, there are many applications which do both. For example, Apple Motion, Adobe After Effects, or Autodesk Combustion. Each one can do some combination of animating stills, drawing shapes, displaying text, and each also comes with tools for doing compositing (keyers, masks, matte manipulation tools, etc.).
In fact, motion graphics often involves compositing. For example, if you think of the title sequence of most James Bond movies, they often involve a combination of silhouettes of people (usually women), hand or computer-drawn graphics, and text. This is a perfect example of how motion graphics involves both graphic design and compositing.
Motion graphics are pieces of digital footage or animation which create the illusion of motion or rotation, and are usually combined with audio for use in multimedia projects It's the industry standard now and it's very important to know the benefits from the clients' perspective. Here is a great resource on that https://yansmedia.com/2d-motion-graphics-is-the-best-animation-style-for-corporate-video-production/