Bueno la "lengua" también te puedes referir al órgano. pero como te han dicho lengua e idioma pueden ser sinónimos

En este contexto son sinónimos.

Like Juan and Jose said, no difference at all Paul. "Lengua" could mean "tongue" and a few more things, but talking about languages, "lengua" and "idioma" are the same. But just so you know, in dictionaries and academic books you'll always see they choose the word "lengua" for it. "Diccionario de la lengua española". But if you're asking someone what language does she talk, you'll never ever use "lengua". "¿Qué lengua hablas?" What the heck...So, if you want to ask someone about it, choose "idioma", okay? "¿Qué idioma hablas?"...and then you say English, Spanish, Boganish and whatever you want.