Also, it's worth noting that computation stack and execution stack need not be the same thing (and, indeed, often aren't).
In CLR, for example, local variables are referenced by index on the execution stack, but you cannot dynamically push new variables onto it - you have to predeclare the locals at the beginning of your execution frame, and the only way to push a new execution frame is by calling another function. On the other hand, opcodes like ADD operate on the computation stack, which is an abstraction completely separate from, and not affected by, the execution stack (every execution frame has its own independent computation stack; there's no way to peek across the boundary).
So in reality it's a bit more complicated - those locals are also kinda like named (or indexed) registers (at least until you take their address). Then the stack adds more temp registers on top of that. In this model, you could always take any register-based code, and translate it to stack-based with a very blunt transform, where something like "ADD x, y, z" becomes "LOAD x; LOAD y; ADD; STORE z". But in addition to that, you also have the flexibility of doing a bunch of operations directly on the temp stack, without intervening stores and loads, that are unavoidable in the register representation. So I would argue that it's the stack representation that is a superset of register one, not the other way around.