The man who never alters his opinions is like standing water, and breeds reptiles of the mind. ~ English poet William Blake
There are 9,547 known reptile species. All breathe air, even those thoroughly adapted to an aquatic lifestyle.
Reptiles have a skin covered in scales and/or scutes. Most lay shelled eggs, though some vipers and constrictor snakes are viviparous (live birth).
All reptiles are considered tetrapods (4-legged). Snakes qualify by their descent from lizards, though they lost their limbs and external ears at the gain of specialized adaptations. The most primitive of the modern snake groups – pythons and boas – retain vestigial hindlimbs, which show as small, horn-like claws at the base of the tail.
Snakes are lizards sans 4 limbs and external ears. But then, lizards don’t necessarily have legs nor external ears. There are worm-lizards that appear as oversized earthworms. The white worm-lizard of South America often forages in the deep galleries where leafcutter ants dump their waste. The larvae of certain beetles pass their own worm-hood there, serving as worm-lizard food when found.
Carl Linnaeus, the father of modern taxonomy, was an incautious observer. He misclassified amphibians and reptiles as a single animal group. Working in species-poor Sweden, Linnaeus’ observation of snakes in the water in the 1740s led him to a facile conclusion.
French zoologist Pierre André Latreille first parceled amphibians and reptiles into separate classes in 1825; a determination popularized by English anatomist Thomas Henry Huxley. Huxley, along with English biologist Richard Owen, clumped “antediluvian monsters” into Reptilia. With this, dinosaurs became reptiles, which isn’t quite right.
German biologist Ernst Haeckel decided it logical in 1866 that vertebrates be divided by respective reproductive strategy; whereupon reptiles, birds, and mammals were united by an amniotic egg. By the end of the 19th century, birds and mammals were excluded from Reptila, as they are endothermic, whereas reptiles otherwise are ectothermic. (Dinosaurs were mesothermic – one of the telling indicators that they do not belong in the reptile class.)
That left reptiles as amphisbaenians (carnivorous worm-lizards of Africa and South America), lizards, tuatara (a unique New Zealand lizard), toads, turtles, alligators & crocodiles, and snakes, along with the fossil groups of dinosaurs, synapsids (mammal-like reptiles), and Permian period pareiasaurs: proto-turtles that were up to 300 cm long and 600 kg. This remains the common definition of the class Reptilia.
It is sloppy classification. Dinosaurs don’t belong, and birds, which descended from dinosaurs, are latter arrivals in the clade of dinosaurs.