My definition is that someone who crafts (or makes) an instrument from bare wood (but may attach bought-in shinyware & electrics) is a luthier .
There's also the term "tech" used; I'd define that as someone who does professional-grade setups and repairs.
In contrast, someone who builds (or assembles) an instrument from pre-made parts (ie. neck & body) isn't; I'd probably call them builders(?).
I've had great results putting together instruments from parts, but my woodworking skills are pretty abysmal, so I could probably never be a luthier.