Specification for br_if mentioning popping of i32.const confuses me

[amn]

At https://webassembly.github.io/spec/core/exec/instructions.html#control-instructions, the definition for br_if specifies:

2. Pop the value i32.const c from the stack.

A stack does not contain "i32.const" values, does it? I understand the implication (at least I think I do) -- there's a 32-bit WA integer typed value on the stack, but why call it "i32.const" -- that's just confusing? Because i32.const is commonly understood to be an instruction.

Why not write "Pop an i32 value c from the stack." instead?

[zapashcanon]

This is explained here

[amn]

@zapashcanon, thank you, I suppose you were pointing me to the following parable, specifically:

In most places of the semantics, values of different types can occur.
In order to avoid ambiguities, values are therefore represented with an abstract syntax that makes their type explicit. It is convenient to reuse the same notation as for the const instructions and ref.null producing them.

Is my understanding correct?