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

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.

(Hope this question is appropriate here. FAQ page at Theoretical Computer Science - Stack Exchange, a research level CS community, indicates that theoretical CS question can be asked here.)

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 RE cstheory FAQ: Well, ComputerScience.SE has gone beta! You can join and post your question there! – user2468 Mar 7 '12 at 19:28 @J.D. thanks, I just got a notification too. For this particular question I've already made myself satisfied. – IsaacS Mar 8 '12 at 1:17

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.