A mug is bigger. :)

Сups are smaller than mugs, so they hold less coffee.

Hola Juan, No sé en Perú, pero en España tomamos el café con leche en una taza. Más estrecha por abajo que por arriba, y con un asa en un lado. Una mug es uno de esos vasos grandes hechos de cerámica igual de ancho por abajo que por arriba, y más altos que una taza. También llevan asa. En España las utilizamos también para colocar los lápices, bolis... Chao

If I do a Google image search on "taza de te," I see, mostly, "cups." If I do a Google image search on "jarro de cafe," I see, mostly, "mugs."

In the United States, a "mug" typically looks like this: almost a cylinder with almost vertical sizes, holding maybe 300 ml, and usually placed directly on the table: http://files.doobybrain.com/wp-content/uploads/2009/03/diner-mug.jpg A "cup" typically looks like this: a hemisphere, holding maybe 200 ml, and usually part of a "cup and saucer." The saucer is the little plate underneath the cup. http://upload.wikimedia.org/wikipedia/en/e/ed/CoffeeCup.svg There are no firm rules, but usually, mugs are informal, and are more likely to be decorated in bright or playful designs, or with humorous pictures or sayings on them: http://tinyurl.com/mx9whoq In honor of Peru, I present this one, which says "Keep calm and read Vargas Llosa." http://tinyurl.com/m7e9j3o