Is the Jazzmaster a Strat neck? // Allparts vs Musikraft neck

I am building a jazzmaster in parts and I am considering a custom Musikraft neck with a flamed maple or an Allparts with some modernizations such as the strunk stripe and the adjustment of the truss rod from the headstock (jzro-mod). I have two crises about building with these arms (besides the price difference) What happens is that I notice that the headstock is bigger than the vintage one, something like the jazzmaster 66 (?) and I'm not sure if that's what I'm looking, since I want to try to recreate one from '59 and I have a suspicion that it's just a strat neck with a jazzmaster decal. Does anyone really know the difference that can guide me with the necks I want to buy? And also, which do you think is more convenient?