If I had to guess, I'd say "box" is a reference to "boxed values" mentioned in many papers about functional language compilation. Typically, the stack of these implementation would either be "unboxed values", or pointers to "boxes" on the heap.
Clearly, some of those folks have worked on ML or Haskell implementations.
> If I had to guess, I'd say "box" is a reference to "boxed values"
Yes, that's the start of it but it was expanded to multiple box classes (and maybe eventually user-defined ones) rather than just boxed and unboxed values: a developer can currently use box(HEAP) and box(GC) (a bare `box` is an alias for `box(HEAP)`)
Clearly, some of those folks have worked on ML or Haskell implementations.