andouille and andouillette are tripe-based sausages, but otherwise they have little in common. The former is generally a large sausage, frequently smoked and eaten cold in slices as a starter; the latter is a small sausage that is never smoked and is generally grilled and served hot as a main dish. There are numerous versions of each. The words may derive from the Latin inductile, meaning something drawn out.
Andouilles were served on the best French tables in the Middle Ages, but in the centuries since then they have mutated into a more rustic sort of speciality. The use of the term andouille as a slang word meaning ‘imbecile’ might seem to fit with this new role, but it is hard to explain and appears to be incompatible with the existence of lively associations of andouille-lovers.