Another distinction is in how "complete" the intentions of the uprising are. A revolution aims to take over the institutions they are revolting against essentially unchanged but with a complete transfer of power to the revolters. For instance the French Revolution aimed to overthrow the monarchy and rule the whole of France in a different way, not to carve out "commune France" and leave "monarchy France" in a different part of the country.
A rebellion can be more localised geographically or have specific aims short of regime change. For instance the South of the US rebelled in an attempt to split from the North, and Dhofar rebelled in an attempt to split from Oman. The various rebellions against Bolshevik rule after the Russian Revolution weren't intended to overthrow the government, but to change aspects of its policy. They still violently usurped political power in individual cities, but never with the intent of seceding from Russia or taking over the whole country. Wat Tyler's rebellion aimed to remove the unpopular parts of the government and Tyler went out of his way to make it clear that the King was to stay no matter what (a unfortunate, painful and ultimately fatal error on his part).
I disagree that the name is based on the success. There are plenty of examples of failed revolutions. There are some uprisings known as rebellions which have been successful, although they're rare - possibly because if they don't completely take over the old government it never gives up fighting. The most recent example is the South Sudanese rebellion which ended in them gaining independence, but I also found the Telangana Rebellion - oddly, an uprising to join an independent territory (Hyderabad) to a larger nation (India).
In short, I think the defining factor is whether the uprising aims to take over an existing polity and replace the rulers, or change policies or borders without taking over the reins of power as they originally existed.
That said, the two terms are essentially synonymous, and any difference is of inference not definition. There are plenty of counter-examples - off the top of my head, the Belgian Revolution meets my definition of a rebellion as it left the rump Netherlands under the original regime. The 1905 Russian Revolution changed the policies and methods of the regime, but left the form and leadership of the Empire mostly unchanged. The various rebellions in Japan during the samurai era usually aimed to take the reins of power in toto, which is how I've defined a revolution. As with anything where politics and history overlap, the words used are more a matter of rhetoric than exactitude, and the name in the history books is usually chosen by the winners.
For amusement, I refer you to the New York Times of August 27, 1861 which considers the difference between the American Revolution (the good guys) and the Southern Rebellion (the bad guys).