I think most programmers probably think it reasonably similar terms - it's just that having working in STLC or a high-level functional language gives you some mental machinery that doesn't rely on decomposing this thought process into some concrete syntax from a programming language.

(incidentally, this is one of the reasons why I think there is a lot of value in learning the Lambda calculus early in a computer science education).

This is what we are really talking about when we claim that reading, e.g., SICP will make you a better programmer even if you don't work in Lisp.

SICP is not a book about Scheme. It's a book about computation that happens to use Scheme. And it is resolutely abstract, encouraging you to think in non-linguistic terms. One of the bits I remember best was near the beginning, when they talk about the shapes of computational processes -- iterative processes have a different shape from recursive processes. Now I use that sort of mental picture all the time.

The goal is to think about software like a mathematician thinks about math. If you're thinking in a language, it's like the way I thought about math when I was nine years old -- to the extent that I knew what a mathematician was, I thought it was someone who was really really good at the long division algorithm. Someone who could subtract really fast!