"Revolution", as defined generally in this context by Merriam-Webster, is "a sudden, radical, fundamental or complete change". In the context of socio-political change, it is a fundamental change in a society's structure, including how and by whom it may be governed, and who benefits most and least from it.
"Rebellion" is generally 1) "Opposition to authority or dominance", and more specifically 2) "an open, armed, and usually unsuccessful defiance of or resistance to an established government". A rebellion is a violent uprising of the masses against their leadership, as opposed to "resistance" in general which can be armed or unarmed and for any goal including marginal OR complete change to a system of government.
Rebellion may cause revolution, but one does not necessarily indicate the other. A leader may for instance abdicate his position of his own free will, and the people, in absence of a leader, may form an entirely new system of government, or may simply choose another person to lead them under the current system. Revolution can also happen by a fundamental change in technology; Eastman Kodak, which invented the digital camera, ironically became the victim of its own invention as the upper management didn't want to cannibalize their extremely profitable film sales. International Business Machines was originally in the business of making typewriters, and the CEO at the time swore that IBM would never make a computer. Luckily for IBM, the upper management saw the error of that way of thinking, and that statement became a humorous byline in the history of a now very successful global computer company, instead of its epitaph.
Rebellion, on the other hand, does not necessarily cause revolution, and as stated in the definition it often doesn't; the violent uprisings that didn't establish a new world order are generally the ones called "rebellions" or "civil wars", while the ones that did are called "revolutions". The French and American Revolutions of the late 1700s were successful rebellions; the subsequent Indian Nation uprisings in the United States were unsuccessful "rebellions".