Microorganisms (and plants) make cysteine from serine using H2S as the sulphur source. Condensation of these two directly gives cysteine in some bacteria, but most often the reaction sequence is:
> serine + acetyl-CoA >>> O-acetylserine + CoA-SH
>
> O-acetylserine + H2S >>> cysteine + acetate + H2O
As you say, in terms of the sulphur, cysteine and methionine are interconvertible.
Animals rely upon their diet for methionine, and can make cysteine from that methionine.