In what sense is “Uniform-cost search” uniform?

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The name of Uniform-cost search in computer science is not instinctive since what part of it being "uniform" is not clear to me. Apparently uniformity is not about the cost of each edge - most of the examples handle edges with various costs. Can someone explain? Thank you.

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Trying to answer to my own question. Correct me if wrong.

I think I need to think about 2 types of concept in search so-called un-informed and informed search, and (here I'm skipping much explanation about fundamentals though) Uniformed Search (don't get confused) can be considered as "uninformed" version of A* search, i.e. return of heuristic function is equal to zero. This zero informed cost might have us call it as uniformed.

This naming is not really intuitive, because the reason it's called as uninformed is based on the heuristic function's cost, not on the path-cost which is the main comparison criteria when you talk about un-informed search.