For practical application there are three basic types of yeast, compressed, active dry and instant.
Compressed is the least normally found because it needs to be refrigerated, it's normally used in commercial bakeries which have storage for a 30-1lb case. Stores find it easier to store active dry or instant.
Compressed and active dry require a double proof, the initial mixing proof then shaping and a final proof prior to baking. Instant can be used as a single proof, but it's easier to shape and work when it's given some initial time after mixing and time to rise.
I keep active dry and instant in the freezer it extends the life of the yeast. There are 'designer' yeasts, Platinum, Bread machine yeast, I don't have experience with those, I stick to basics.
Different yeasts also require different ratios, compressed needs the greatest amount, then active dry, then instant in proportion of yeast to dough for successful production.
In terms of temperatures compressed doesn't care, instant will work when introduced dry into the mix, active dry needs to be dissolved in warm (90-105) liquid, a bit of sugar to kick it before being introduced to the dough.