Plaza principal vs. plaza mayor
The Spanish terms plaza principal and plaza mayor both translate to main square, but they differ slightly in usage and geography. The term plaza principal is a functional description used broadly, especially in Latin America, to point out a town's most important square. On the other hand, plaza mayor is often a historical designation or an official proper name, used most prominently in Spain and historic colonial cities.
Plaza principal
The phrase plaza principal is a general, descriptive term used to indicate the primary or most important square of a town, usually based on its central location or everyday function.
Nos vemos en la plaza principal del pueblo a las cinco.
(We will meet in the main square of the town at five.)
La plaza principal tiene una fuente muy hermosa en el centro.
(The main square has a very beautiful fountain in the center.)
Todos los domingos hay música en vivo en la plaza principal.
(Every Sunday there is live music in the main square.)
El ayuntamiento está ubicado justo frente a la plaza principal.
(The city hall is located right in front of the main square.)
Los turistas siempre visitan la plaza principal para tomar fotografías.
(Tourists always visit the main square to take photographs.)
Plaza mayor
The phrase plaza mayor refers to the historical main square of a city and is frequently used as its official proper name, carrying a sense of tradition and architectural heritage, particularly in Spain.
Comimos unos bocadillos deliciosos en la plaza mayor de Madrid.
(We ate some delicious sandwiches in the main square of Madrid.)
La plaza mayor conserva intacta su arquitectura colonial original.
(The main square preserves its original colonial architecture intact.)
El mercado medieval se celebra cada año en la plaza mayor.
(The medieval market is held every year in the main square.)
Caminaron por la plaza mayor admirando los antiguos balcones.
(They walked through the main square admiring the old balconies.)
La plaza mayor de Salamanca es famosa por su belleza nocturna.
(The main square of Salamanca is famous for its nocturnal beauty.)
Summary
In short, use plaza principal as a general, everyday description for the functional center of a town, which is very common in Latin America. Use plaza mayor when referring to the historical, traditional, or officially named central square of a city, a term heavily used in Spain.