How do credit scores work, and why do they vary between different reporting agencies?

Question

How do credit scores work, and why do they vary between different reporting agencies?

In: Economics

Answer 1

ELI5 why are they considered so fundamental in the US yet aren’t used at all in so many other places (or rather – banks and others can rate my ability to repay debt without checking a history)?

Here my “credit score” is basically a formula based on my income, debt and expenses (living costs, family situation) and of course any past failures to pay bills. But not on past ability to successfully pay my bills or how long I had a credit card.