The Spanish verb 'rehogar' (to sauté) comes from combining the Latin prefix 're-' (meaning 'again') with the Spanish verb 'ahogar' (to cook on low heat). The base verb 'ahogar' itself derives from Latin 'focus' meaning 'fire' or 'hearth'. The evolution from a word about fire/hearth to cooking makes intuitive sense, as cooking was traditionally done over a hearth's fire. The addition of 're-' suggests the repetitive or thorough nature of sautéing, where ingredients are repeatedly moved around in the pan over heat.

A simpler related Spanish word is 'ahogar', which means 'to cook on low heat' or in modern Spanish can also mean 'to drown' or 'to smother'. While 'rehogar' specifically refers to sautéing, 'ahogar' is a more general term for slow, low-heat cooking. The connection between these cooking terms and the meaning 'to drown/smother' likely comes from the idea of food being immersed in liquid or covered while cooking.

The Latin word 'focus' that gave rise to these Spanish cooking terms has also made its way into English, though with quite different meanings. The English word 'focus' comes from the same Latin root, but instead of developing cooking-related meanings, it took on the sense of a central point or concentration. This meaning likely developed from the idea of a hearth being the central gathering point in a home. We can also see this Latin root in words like 'focal' and 'focalize'.