Origins
The word 'deer' is one of the most famous examples of semantic narrowing in the English language. Today it denotes a specific family of hoofed mammals (Cervidae). In Old English, 'dēor' meant any animal, any wild beast, any living creature. German 'Tier' (animal), Dutch 'dier' (animal), Swedish 'djur' (animal), and Old Norse 'dýr' (beast, animal) all preserve the original broad meaning. English alone narrowed the word to a single type of animal.
The word descends from Proto-Germanic *deuzą (animal, beast), from PIE *dʰeus- (to breathe, to blow), making the deer, etymologically, 'the breathing thing' — a living creature, defined by the quality of being alive, of drawing breath. This PIE root also appears in other words related to breath and spirit, though the connections are debated.
The narrowing from 'any animal' to 'cervid' occurred gradually between the 11th and 16th centuries. After the Norman Conquest of 1066, French loanwords flooded into English: 'animal' (from Latin 'animālis,' having breath, from 'anima,' breath/soul), 'beast' (from Latin 'bestia'), and 'creature' (from Latin 'creātūra') all competed with native 'dēor' for the general meaning of 'living thing.' Simultaneously, deer-hunting became the supreme aristocratic sport of Norman England. The royal forests were established primarily as deer reserves, and elaborate Forest Laws punished poaching with mutilation or death. 'Deer' became so strongly associated with the hunted animal of the forest that it gradually lost its broader meaning.
Literary History
Shakespeare, writing around 1600, could still occasionally play on the word's older sense — in King Lear, Edgar calls mice 'small deer.' But by the 17th century, the narrowing was essentially complete.
The word 'wilderness' preserves the older meaning of 'dēor.' It comes from Old English 'wilddēornes,' literally 'wild-deer-ness' — 'the place of wild animals,' 'the condition of being among wild beasts.' When the Pilgrims described America as a 'wilderness,' they were saying, etymologically, 'a place full of wild animals' — not 'a place with no people' (the common modern misunderstanding).
The word 'reindeer' is partially redundant: it comes from Old Norse 'hreindýri,' where 'hreinn' meant reindeer and 'dýr' meant animal. 'Reindeer' is thus 'reindeer-animal' — the species name plus the generic word for animal. The first element 'rein-' may derive from a Sami or other Finno-Ugric language.
Old English Period
The flesh of the deer is called 'venison,' from Latin 'vēnātiō' (hunting, the chase, game meat), from 'vēnārī' (to hunt). This French-Latin term for deer meat, replacing any native English term, is another consequence of the Norman Conquest — the animal was English 'deer,' but its meat was French 'venison,' just as the cow is English but its meat is French 'beef' (boeuf), and the pig is English but its meat is French 'pork' (porc). The social stratification is embedded in the vocabulary: the Anglo-Saxon peasant tended the living animal, the Norman lord ate its flesh.