Not really. Look at the definitions of the two words. Merriam Webster's Dictionary defines "revolution" as " fundamental change in political organization; especially : the overthrow or renunciation of one government or ruler and the substitution of another by the governed". It defines "rebellion" as "open, armed, and usually unsuccessful defiance of or resistance to an established government."
The Revolutionary War accomplished it's goal. The outcome of it was a break with Britain and the substitution of their rule with our own government. It was, in short, successful.
The Southern Rebellion did not accomplish it's goal. It was certainly open and armed, but it was also unsuccessful. It was a dismal failure, as the definition states.
So the Revolutionary War is the appropriate title, as is the Southern Rebellion. Now, maybe if you had won you could have called it the "Southern Revolution" or the "Second American Revolution". But you didn't. You're losers.
The "Revolution" is actually a misnomer. The people in power in the Colonies before the "revolution" were the same people in power in the Colonies after the "revolution."
I learned years ago that the most accurate description for that event is "The American War for Independence. "
The Southern Rebellion did not accomplish it's goal.
Neither would have the Colonists had George III been as determined as Lincoln. He had the power to crush them. He chose not to do so.