volver vs regresar
Both mean 'to return' — volver is universal Spanish, regresar is more Latin American and slightly more formal.
volver
To return, to come back — the standard word in Spain and widely used everywhere.
Vuelvo en seguida.
I'll be right back.
One of the most useful phrases. Regresar would work but sounds slightly stiff here.
Volver a + infinitivo = to do something again.
Volvió a llamar = He called again.
Volver a + infinitive is how Spanish says 'again.' Extremely useful structure.
¿Cuándo vuelves?
When are you coming back?
Natural in all registers. The default return verb in Spain.
regresar
To return/go back — preferred in much of Latin America, more formal in Spain.
Regresaron al pueblo de sus padres.
They returned to their parents' village.
Sounds slightly more formal or literary than volvieron. Both correct.
Ya regresé.
I'm back.
Common in Mexico and much of Latin America where regresar is the natural word.
No hay vuelta atrás.
There's no going back.
Vuelta (noun from volver) in an idiom — regresar doesn't have this idiomatic reach.
Tricky bit
Volver has far more idiomatic reach: 'volver en sí' (to come to/regain consciousness), 'volver loco' (to drive mad), 'volver a ver' (to see again). Regresar can't do any of these. Learn volver first.