Sorry for the confusion. In fact those are *both* belt nesting numbers and stack frame numbers!
The problem is that internally (where we who work on the Mill live) each thread actually has two stacks that are disjoint in the address space, whereas a conventional has only one. One of the two Mill stacks is the data stack, rooted in the initial stacklet, and containing content that is addressable by the application. Logically each call adds a new data stack frame, but a frame may be empty and have no content.
The second stack is the spiller stack, rooted in the initial spillet. It’s content is not application-addressable (debuggers etc. go through a special library to get at it). Each call adds a new spiller stack frame, which is never empty.
So those numbers are both belt nesting numbers and spiller stack frame numbers, which are in fact the same thing. And they are also data stack frame numbers, but some data stack frames are invisibly thin.