Desfile vs. parada
In Spanish, both desfile and parada can be translated as "parade," but they are used in very different contexts. While desfile is the universal term for almost any type of public procession, parada is generally restricted to formal military contexts or is used in specific regions as a direct borrowing from the English language.
Desfile
The word desfile is the standard, most common, and universally understood term for a parade in Spanish. It is used to describe festive celebrations, fashion shows, school marches, holiday processions, and any public event where people, vehicles, or floats move forward in a line.
Fuimos al centro de la ciudad para ver el desfile de carnaval.
(We went downtown to see the carnival parade.)
El famoso diseñador presentó su nueva colección en un desfile de modas.
(The famous designer presented his new collection in a fashion parade.)
Los niños decoraron sus bicicletas para el desfile de primavera del colegio.
(The children decorated their bicycles for the school's spring parade.)
Miles de ciudadanos salieron a las calles a disfrutar del desfile de Acción de Gracias.
(Thousands of citizens took to the streets to enjoy the Thanksgiving parade.)
El equipo campeón celebró su victoria con un desfile por la avenida principal.
(The champion team celebrated their victory with a parade down the main avenue.)
Parada
In standard Spanish, a parada refers strictly to a military parade or a formal review of troops. However, in communities with a strong English influence, such as Puerto Rico or among Spanish speakers in the United States, parada is often used interchangeably with desfile to mean any public parade, acting as a direct calque from English.
El presidente pasó revista a las tropas durante la parada militar.
(The president reviewed the troops during the military parade.)
Todos los años mi familia asiste a la Parada Puertorriqueña en Nueva York.
(Every year my family attends the Puerto Rican Parade in New York.)
Los aviones de combate sobrevolaron la ciudad como parte de la gran parada nacional.
(The fighter jets flew over the city as part of the grand national parade.)
Los canales de televisión transmitieron la parada militar de las fuerzas armadas en vivo.
(The television channels broadcasted the armed forces military parade live.)
El general organizó una parada en la base para honrar a los soldados caídos.
(The general organized a parade at the base to honor the fallen soldiers.)
Summary
To summarize, you should use desfile for everyday parades, festive celebrations, and fashion shows, as it is the universally correct word in Spanish. You should only use parada when discussing a formal military parade, or when referring to specific cultural events in regions where English has influenced the local Spanish vocabulary.