I've recently gotten interested in the monarchies of the Americas and I noticed that after leaving Spain, Mexico was a monarchy under an emperor for a while. When the French returned the monarchy, they revived the title of Emperor. What were the reasons for using that term instead of the more common King/Kingdom?
By declaring Mexico an empire they were recognizing the unique character of the different areas. The hope was that by offering a form of federalism the peripheral areas like the Yucatan, Tamaulipas, and maybe the Kingdom of Guatemala and other Central American states would be satisfied and stay with the nascent empire. Basically it was chosen because it was the appropriate word for a monarchal state comprised of a variety of disparate peoples, provinces, and kingdoms.
The imperial court then betrayed the idea of a monarchal federal state by trying to enforce a more rigid central top-down style of rule. The first empire was short lived, and saw most of the peripheral areas all make bids for a separate independence. Some of these were more successful than others.
When the French came and established the second empire, they were just restoring what had by then been the "traditional" titles of monarchal rule, however short lived.
Source Forging Mexico by Timothy Anna