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Marrón vs. moreno

In Spanish, while both marrón and moreno can relate to shades of brown, they are not interchangeable. Marrón is the specific name for the color brown, used for objects, while moreno describes the complexion or hair color of a person.

Marrón

A1
This is the direct translation for the color brown. It is used to describe the color of inanimate objects, animals, and features like eyes. Using marrón to describe a person's skin tone is very unusual and can be considered pejorative.
La mesa de madera es de color marrón oscuro.
(The wooden table is a dark brown color.)
Me compré un abrigo marrón para el invierno.
(I bought a brown coat for the winter.)
El perro tiene el pelo marrón y los ojos negros.
(The dog has brown fur and black eyes.)
Sus ojos son de un tono marrón claro muy bonito.
(Her eyes are a very beautiful light brown shade.)
En otoño, las hojas se vuelven de color marrón.
(In autumn, the leaves turn brown.)
¡Qué marrón tener que arreglar esto ahora!
(What a hassle to have to fix this now! (Colloquial use in Spain for a problem or a hassle).)

Moreno

A1
This word is used almost exclusively to describe people. It can mean having dark hair (brunette), being tan from the sun, or having a naturally darker complexion. It is never used to describe the color of an object.
Después de dos semanas en la playa, estoy muy moreno.
(After two weeks at the beach, I am very tan.)
Mi hermano es alto, delgado y moreno.
(My brother is tall, thin, and dark-haired/dark-skinned.)
La chica morena que está sentada allí es mi prima.
(The brunette girl sitting over there is my cousin.)
A ella le gusta tomar el sol para ponerse morena.
(She likes to sunbathe to get a tan.)
Busco a un hombre guapo y moreno.
(I'm looking for a handsome, dark-featured man.)
¿Prefieres a los chicos rubios o a los morenos?
(Do you prefer blond guys or dark-haired guys?)

Summary

In short, the key difference is what is being described. Use marrón for the color of things, animals, or eyes. Use moreno for a person's tan, skin complexion, or dark hair. Remember this simple rule: things are marrón, people are moreno.