In terms of solid bodied guitars and basses I'd say that if you're making the neck by hand then you're a luthier; cutting and routing the body from a block of wood is mere carpentry ; and putting a bitsa together from aftermarket parts is no harder than putting together the average Airfix model kit - the finishing is the hardest bit - and doesn't really warrant any specialist job description.
Yes, as said above the word "luthier" is derived from a maker of lutes; I believe the word "lute" itself derived from the Arabic for gourd: oud (which in dried form made the backs for the ancestral instruments). Subsequently extended to guitar and violin making throughout Europe - although interestingly in Spain, the apex and epicentre of guitar building, a master such as Ramirez or Contreras would be called a "Constructor de guitarras", which is really more descriptive.
Thanks to Maggie Thatcher giving me some spare unemployed time over 40 years ago I've completed lute-making, guitar-making, and violin-making courses, which were hugely enjoyable and character-building, so I guess I could call myself a luthier but wouldn't have the cheek to do so. Very helpful for building bitsas though, and did make one bass from scratch;; a fretless Stingray (that was enough!).