Language / What is the name for "I would", is it conditional mood or something else? [12]

Well, actually there could be a difference between 1st and 2nd conditional in polish.

If / when she calls me, I'll go. - Jak do mnie zadzwoni, pójdę.

If she called me, I would go. - Jeśli / gdyby do mnie zadzwoniła, poszedłbym / poszedłabym.

There is a slight difference between jeśli, gdyby and jak. "jak" is usually used if something's going to happen sooner or later. If you doubt, that

she will call you at all
then you should use "jeśli / gdyby".

And I would rather use "gdybym" instead of "jeśli" if I want to create 3rd conditional.

So:
1st conditional => jak
2nd => jeśli
3rd => gdyby

For instance, you shouldn't say:
Gdybyś podgrzał(a) wodę, to się zagotuje = If you heat the water, it boils.
Because it literally sounds like 3rd conditional.
People usually say: jak / jeśli podgrzejesz wodę, to się zagotuje.

And I think that "jak" is the most universal phrase in polish conditionals.

But it's just a detail, so not to worry if you mix "jak / jeśli / gdyby" up.