Vamos. means Let's go. Vamos a la playa. Let's go to the beach. OR: We're going to the beach.
Nos vamos. means: We're leaving or going (away from a place). OR: Nos vamos a la playa. We're leaving for the beach.
That is, when these phrases are used in speech like that.
irse, the reflexive verb can be go or leave but if you mean leave you need it.
- Me voy ahora. I'm leaving now. I'm going now. To leave or go away from a place: irse.
To say leave use irse. Both irse and ir though mean go.
¿ Dónde está José? Se fue. [He left.]
¿ Dónde están José y Mária? Se fueron. Se marcharon. [They left.]