Carta is the Spanish word for menu, while men usually refers to the men del da. Many restaurants in Spain offer a men (fixed price lunch menu) that may not be advertised.
Carta is Latin and Italian for "paper" and is Spanish and Portuguese "letter". In English it takes the form "card" or "chart". Most of its uses pertain to its meaning as "paper", "chart", or "map", for example in Magna Carta.