The American colonists staged their Revolution against the British in pursuit of rights which they believed had been taken away from them by the mother country. The colonists regarded themselves as beneficiaries of the ancient rights and liberties enjoyed by successive generations of Englishmen. Yet these very same rights and liberties were now under threat from the British government, which according to the colonists was engaging in tyrannical behavior.
One could argue, then, that the American Revolution was conservative, in that it sought the reestablishment of rights and liberties that had supposedly existed since time immemorial. In that sense, it was rather like the Glorious Revolution of 1688, which drove James II from the throne and replaced him with King William and Queen Mary. Just like the American colonists of almost a hundred years later, those participating in the Glorious Revolution didn't see themselves as dangerous radicals or subversives. They were conservatives restoring an ancient constitutional settlement that was under threat.
The French Revolutionaries, on the other hand, consciously sought to remove an existing political order that had existed for centuries and replace it with an entirely new system based on abstract rights. They were not, unlike the American Revolutionaries, restoring specific rights, but creating new ones. They wanted abstract human rights derived from a radically liberal political philosophy.
Even in its relatively peaceful early stages, then, the French Revolution was a good deal more radical than that which had convulsed America just over a decade before. As the rights on which the French Revolutionaries insisted were abstract, they had no actual roots in society. This meant that those rights somehow had to be imposed on the people. But this was easier said than done in a country which was now being attacked from all sides by the crowned heads of Europe.
Once the Revolutionary War was underway, leadership of the Revolution passed to the radical Jacobin faction. The Jacobins proceeded to instigate a reign of Terror against all alleged enemies of the Revolution. It was this radical, bloody phase of the Revolution that turned many of its former supporters against it, including many in the United States who had originally seen parallels between the struggles of the American colonists and the French Revolutionaries.