Español Cuando estaba estudiando Español, aprendí que let's go es vamos, pero cuando fui a México, lo único que oí era vámonos. Le pregunté a una persona bilingüe allá, pero no supo la diferencia...
Nos vamos seems to be derived from irse whereas vamos is derived from ir, and hence nos vamos means we leave whereas vamos means we go. The "tell" (for me) is the "reflexive modifier", i.e. the "se" in irse and the "nos" in nos vamos, which establishes/enforces the relationship between the two.
ir plays triple duty, being used to construct the periphrastic future, to indicate motion, and occasionally to construct nosotros/as commands. Only two of these three are mutually exclusive, so we get two potential interpretations with vamos a ir a ver. The first ir can either set up the future or, thanks to being specifically the form vamos (a shortened form of vayamos), it can also ...
This passage from DPD explains why "vamos" is used as an alternative of "vayamos" for imperative, first person plural: La forma vamos es hoy la primera persona del plural del presente de indicativo: «Laureano y yo nos vamos al jardín» (Gallego Adelaida [Esp. 1990]); pero en el español medieval y clásico era, alternando con vayamos, forma de primera persona del plural del presente de ...
vamos was in medieval Spanish another form for first person plural of present of subjunctive. that is to say: both vamos and vayamos were used in that case. vamos was also used (as well as today) as first person plural of present of indicative. nowadays, the only "vestige" of that old use for vamos is the fact that it is also used as imperative plural for the first person.