Reminds me of my favorite math essay: "When is one thing equal to some other thing?"
It's a great question, much deeper and more interesting than it seems. The essay suggests thinking in terms of isomorphisms (relative to the structure you care about) rather than equality in some absolute sense, and I've found a fuzzy version of that to be a really useful perspective even in areas that can't be fully formalized.
Mathematics is all just explanations for why this is really that. If it didn't have to respect its human audience, and their failure to grasp similarities, the whole edifice could be one implicit statement. (After all, since this is really that, there is no this or that.) So mathematics is about people.
I jumped to a similar conclusion right away and popped over here to comment only to find you have beaten me to the punch. I use to keep a work wiki page of common problems the team encounters over and over again.
Years ago, I stumbled upon the "idea" was already debated in other fields long before programming. Lumpers and Splitters.
It's a great question, much deeper and more interesting than it seems. The essay suggests thinking in terms of isomorphisms (relative to the structure you care about) rather than equality in some absolute sense, and I've found a fuzzy version of that to be a really useful perspective even in areas that can't be fully formalized.
https://people.math.osu.edu/cogdell.1/6112-Mazur-www.pdf