Ah, maybe, but isn't there generally exactly one latin character
corresponding to one cyrillic character, even if not the ones that
look similar?

Not exactly, it is usually much more complicated (but I don't think
that I can reproduce it well in this encoding).

Some tricky differences a
Russian "A" is pronounced as English "uh"
Russian "B" is equivalent to English "V"
Russian "C" is equivalent to English "S"
Russian "E" is pronounced to English "eh"
Russian "P" is equivalent to English "R"
and so on

And one letter to one letter does not always work:
(trying cyrillic characters)
ý is pronounced as English "shch" ("sh" + "ch" quickly)

A 15 centuries old mess ;-)