Nope, box modelling is a flavor of sub-D modelling. A term used mostly back in the days when there was still “solid poly software” (meaning things were always watertight and closed, no open faces. Wings 3D was probably the most well known box modeller). Back then the only option was to literally cut your model from a box. On the other hand you had software like Maya that was able to do something like “poly by poly” modelling. But both are poly- or SubD modelling. Nowadays classic box modelling as a technique nearly died out, though, because a workflow like that is unnecessary with today’s tools.
That you wouldn’t “recommend” to be able to do nurbs and polys at the same time is pretty ridiculous. That’s like saying: “I don’t recommend people who sketch to also get into painting because the approach is just so different…” what is that even supposed to mean??
I think you got that wrong. SubD basically IS T-Splines. The T-Spline system is more or less an adaption of SubD modelling for the CAD World. Before I got into industrial design I worked in entertainment for a while… so actually I am one of those rare people who can do subD, Zbrush and at the same time SolidWorks 
To clear things up and simplify them:
- CAD Software
e.g. SolidWorks
1.5 A blend of both - e.g. Fusion 360
- SubD Software
e.g. Maya
2.5 A blend of both - e.g. Modo
- Sculpting Software
e.g. Zbrush
So I do understand that one might find it strange of Fusion to call it sculpting because in industry terms it simply IS NO SCULPTING (which indeed is really like digital clay) but SubD/T-Spline modelling (which is almost identical) modelling.
I think Fusion is also not helping it’s users to understand the modelling tools they provide by that weird terminology. There are only a handful of tutorials on “Fusion sculpting” but there are literally a million tutorials on SubD modelling. People need to realize that in order to use SubD/T-Splines the right way you have to learn how to properly do it and that is best done with classic SubD tutorials. Then again I am even shocked how little the Fusion guys themselves know about SubD because whenever they show some “sculpting tutorials” on their YouTube channel I get a headache and want to scream at them “this is not how you f******ing do it!”.
By the way I know for a FACT that some big German car manufacturers are using SubD for their concept cars and digital explorations. The data SubD is providing can be easily used for things like CNC milling and it is much much much faster and more intuitiv than software like Alias. The software of the car industrie’s choice is Maya for now. This is a fairly recent trend and I am sure we are also going to see a lot more SubD modelling in the industrial design industry.