The word 'stray' entered English in the 13th century from the Anglo-Norman French 'estrayer', which carried the sense of wandering or becoming lost. This French term itself evolved from the Vulgar Latin 'extravagare', a compound verb formed from the Latin preposition 'extra' (meaning 'outside of, beyond') and 'vagari' (meaning 'to wander'). The literal idea of 'wandering outside' or 'wandering beyond proper bounds' is preserved in the modern meanings. Over time, this concept of wandering from a proper place or path was applied first to physical movement, then to animals separated from their owners, and finally abstracted to describe thoughts or discussions that digress from a main topic.

The word 'stray' is a simplex word derived from the Anglo-Norman French 'estrayer', meaning 'to wander'. Its ultimate origin is the Latin 'extra', meaning 'outside of', via the Vulgar Latin 'extravagare', which is the source of the English word 'extravagant'.