The point is that it varies between calls to a function, rather than within a call. Consider, for example, a name for a value which is a pure function (in the mathematical sense) of the function's (in the CS sense) inputs.
What's happening is that each iteration of the loop these are new variables but they have the same name, they're not the same variables with a different value. When a language designer assumes that's the same thing the result is confusing for programmers and so it usually ends up requiring a language level fix.
e.g. "In C# 5, the loop variable of a foreach will be logically inside the loop"
In C the first needs us to step outside the language to the macro pre-processor, the second needs the keyword "const" and the third is the default
In Rust the first is a const, the second we can make with let and the third we need let mut, as Carmack says immutable should be the default.
The point is that the word "variable" inherently reflects change. And choosing it (a-la your malapropism-that-we-all-agree-not-to-notice "immutable variables") to mean something that does (1) is confusing and (2) tends to force us into worse choices[1][2] elsewhere.
A "variable" should reflect the idea of something that can be assigned.
[1] In rust, the idea of something that can change looks like a misspelled dog, and is pronounced so as to imply that it can't speak!
[2] In C++, they threw English out the window and talk about "lvalues" for this idea.
fn sin(x: f64) -> f64 {
let x2 = x / PI;
...
Anyway this is kind of pointless arguing. We use the word "variable". It's fine.
Those are synonyms, and this amounts to a retcon. The computer science term "variable" comes directly from standard mathematical function notation, where a variable reflects a quantity being related by the function to other variables. It absolutely is expected to "change", if not across "time" than across the domain of the function being expressed. Computers are discrete devices and a variable that "varies" across its domain inherently implies that it's going to be computed more than once. The sense Carmack is using, where it is not recomputed and just amounts to a shorthand for a longer expression, is a poor fit.
I do think this is sort of a wart in terminology, and the upthread post is basically right that we've been using this wrong for years.
If I ever decide to inflict a static language on the masses, the declaration keywords will be "def" (to define a constant expression) and "var" (to define a mutable/variable quantity). Maybe there's value in distinguishing a "var" declaration from a "mut" reference and so maybe those should have separate syntaxes.