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Siguiente vs. próximo

While both siguiente and próximo can be translated as next in English, they are not interchangeable in Spanish. The key difference lies in whether you are referring to the next item in a sequence or the next item in time or space.

Siguiente

A1
The word siguiente refers to the next item in an established sequence, order, or list. It is best translated as the following or the one that comes immediately after the current one.
El siguiente paciente puede pasar, por favor.
(The next patient can come in, please.)
Abre el libro y lee el siguiente párrafo.
(Open the book and read the following paragraph.)
Después de esta parada, nos bajamos en la siguiente.
(After this stop, we get off at the next one.)
¿Quién es el siguiente en la fila?
(Who is the next one in the line?)
El primer paso es mezclar los ingredientes; el siguiente es hornear la masa.
(The first step is to mix the ingredients; the next is to bake the dough.)
La respuesta a tu pregunta se encuentra en la página siguiente.
(The answer to your question is on the following page.)

Próximo

A2
The word próximo generally refers to the next item in a temporal sense (time) or a spatial sense (proximity). It is used for upcoming events, future time periods, or to describe the nearest location.
El próximo verano viajaremos a Italia.
(Next summer we will travel to Italy.)
La próxima reunión del club será el jueves.
(The next club meeting will be on Thursday.)
¿Dónde está la estación de metro más próxima?
(Where is the nearest subway station?)
Espero verte en nuestro próximo encuentro.
(I hope to see you at our next get-together.)
El próximo año empezaré la universidad.
(Next year I will start university.)
El autobús próximo a llegar es el que va al centro.
(The next bus to arrive is the one that goes downtown.)

Summary

In summary, use siguiente when referring to what follows immediately in a sequence, order, or list (the following one). Use próximo when talking about something that is upcoming in time (next week, next year) or what is nearest in physical space. While la semana siguiente (the following week) and la próxima semana (next week) can sometimes be used interchangeably, próximo is far more common for future time references.