If King Louis XVI was the abolition of France's monarchy, why were there Kings after him?

After Louis was killed, France was in political turmoil. They had the "Reign Of Terror" which lasted 13 years. In which many of the Aristocracy was beheaded, mostly by the acting government head Robespierre. A during a power vacuum Napoleon seized power over France. After many wars he Crowned him self Emperor of France. This lasted till he was exiled to the Island of Elba, in which he stayed there for a "Hundred Days" In that time the Bourbon's tried to reestablished there Dynasty by crowning Louis the XVIII brother of the XVI. But Napoleon returns and over throws him to re-seize power again. Only for him to be defeated at Waterloo and spend the rest of his life in St, Helena. There was a Louis the XVII but he was never crowned.