The connotation is simply an internal process of indeterminate length rather than one of reflexive length. So they don’t apply it when a GPU is slinging out 120 FPS in a first person shooter.
But now, I see this: the truth is static and non-profit, but calculating something can be sold again and again, if you have a hammer (processing) everything looks like a nail, to sell well the word thinking had to be used instead of excuse for every time results being different (like the shadows) - then, we can have only things that let someone else keep making profits: JS, LLM, whatever.. (just not.. "XSLT" alike).
(yet, I need to study for your second sentence;)
(In math class I've been told that not some number but the formula is the expected result..
.. then people are now asking: "Just show me the prompt instead !" and.. done. ;) )