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Bandeja vs. charola vs. azafate

The Spanish words bandeja, charola, and azafate all translate to the English word tray, but their differences primarily come down to regional dialects and geography rather than distinct physical differences.

Bandeja

The word bandeja is the standard, most common, and universally understood term for a tray across all Spanish-speaking countries, used for serving food, holding items, baking, or even referring to an email inbox.
El camarero trajo las bebidas en una bandeja de plata.
(The waiter brought the drinks on a silver tray.)
Tienes un mensaje nuevo en tu bandeja de entrada.
(You have a new message in your inbox.)
Hornea las galletas en una bandeja para hornear durante diez minutos.
(Bake the cookies on a baking tray for ten minutes.)
Por favor, pon los platos sucios en la bandeja.
(Please put the dirty plates on the tray.)
Ella organizó sus joyas en una pequeña bandeja de madera.
(She organized her jewelry on a small wooden tray.)

Charola

The word charola is the preferred and most frequently used term for a tray in Mexico and some neighboring regions, carrying the exact same everyday meaning as bandeja but restricted to specific local dialects.
Pásame esa charola con pan dulce, por favor.
(Pass me that tray with sweet bread, please.)
El mesero dejó caer la charola llena de vasos.
(The waiter dropped the tray full of glasses.)
Necesitamos una charola de aluminio para asar el pavo.
(We need an aluminum tray to roast the turkey.)
Coloca la charola en el centro de la mesa para que todos puedan alcanzar los bocadillos.
(Place the tray in the center of the table so everyone can reach the snacks.)
En el hospital, le llevaron el desayuno en una charola de plástico.
(At the hospital, they brought his breakfast on a plastic tray.)

Azafate

The word azafate is a traditional and highly regional term for a tray used primarily in parts of Central America and Andean countries like Peru and Colombia, often referring specifically to a shallow serving tray with a raised rim.
Mi abuela sirvió el café y las tazas en un hermoso azafate antiguo.
(My grandmother served the coffee and cups on a beautiful antique tray.)
Pon los bocaditos en el azafate antes de que lleguen los invitados.
(Put the snacks on the tray before the guests arrive.)
Ella compró un azafate de mimbre para decorar la sala.
(She bought a wicker tray to decorate the living room.)
El mozo llevó las botellas de agua en un azafate de acero inoxidable.
(The server carried the water bottles on a stainless steel tray.)
Por favor, limpia el azafate después de servir el postre.
(Please clean the tray after serving the dessert.)

Summary

In summary, bandeja is the universal and standard word for tray understood everywhere Spanish is spoken. The word charola is the preferred regional equivalent used almost exclusively in Mexico. Meanwhile, azafate is a more traditional regional variation used in parts of Central and South America to describe a serving tray.