The Spanish word 'cuate' comes from the Nahuatl (Aztec) word 'coatl', which had the meanings of both 'snake' and 'twin'. In modern Spanish, 'cuate' has evolved to mean 'friend' or 'twin', dropping the serpentine association but retaining the connection to pairs or close relationships. This semantic shift from 'snake/twin' to 'friend/twin' likely developed through the concept of close bonds and inseparable pairs, as twins are naturally very close, much like close friends.

Since 'cuate' comes from Nahuatl rather than Latin or Greek roots, there aren't many etymologically related simpler Spanish words. However, in Mexican Spanish, you might encounter variations like 'cuatacho', which is an even more colloquial term for 'friend' derived from the same root.

There aren't any etymologically related English words since 'cuate' comes from Nahuatl, an indigenous language of Mexico, rather than from Indo-European roots that English and Spanish often share. However, English speakers might find it helpful to remember that 'cuate' can mean both 'twin' and 'friend' - similar to how we might call someone our 'twin' in English when we feel very close to them or share many similarities.