I disagree that talking about equivalence or isomorphism would be clearer, simply because those two terms are ambiguous. They each have multiple definitions, w

I disagree that talking about equivalence or isomorphism would be clearer, simply because those two terms are ambiguous. They each have multiple definitions, whereas, as far as I'm aware, alpha conversion only has one. You are correct in your interpretation. I'm not making a song or a dance about alpha conversion, I'm simply using it for description because it is a well-defined notion with a precise meaning. I don't see the point in trying to come up with some other term that means the same thing, when a perfectly good term is already available. Anyway, I appreciate that you are trying to be helpful, but I stand by my phrasing :)