Personal pet peeve of mine as this right-left paradigm is based on the old European standards that is almost the opposite of the US view. What they were 'conserving' in the 19th Century Europe when this right-left labeling came in style, was the old monocrachy, authoritarian system. The 'left' were those of the enlightenment promoting individual liberty.
In the US, it was opposite as we were founded on the enlightenment basis of individual liberty. That Constitutional foundation is what we were trying to 'conserve'. The left here want to move away from that foundation back to a centralized ruler class like Europe.
PPP of mine too. You've got it almost but not quite right.
The term originated in 18th century Europe, albeit very late in the century.
The Right was indeed the party of the Ancien Regime, the defenders of aristocracy, Crown and Church.
However, the Left, while opposed to the Right, was not anything American conservatives would recognize. They believed not in the rights of individuals, but in the rights of The People, acting through its General Will, a mysterious decision made by The People as a whole, interpreted of course by the spokesmen.
No individual had any rights as against The People, which of course in practice meant the State and those in control of it.
The Left was actually much closer to modern totalitarianism than the Ancien Regime, which recognized religious and customary limits on what the King had a right to do.
Meanwhile, in America our Revolution was based on the rights of individuals to live their lives as they saw fit, an ideology descended from Magna Carta and the Whig tradition in English politics. This right to freedom originally applied only to aristocrats, but gradually expanded to include more and more people, till by the time of our Revolution it included most if not perhaps all white men.
There had been a similar tradition in France and other European countries, but it was utterly destroyed as a force in political life by Louis XIV and other monarchs. Lafayette and others tried to promote it at the time of the Revolution, but the ideal was so eroded they could get no traction with The People and were quickly forced into exile or executed. (Same thing happened in the Russian Revolution, BTW.)
That's why the European Right is very different from the American Right, while the two Lefts are the same.
In actual fact, our conservatism descends from a political tradition utterly separate from the European Right/Left dichotomy.