I'm looking at this bread recipe and it says to use "Bakers Yeast" but when I make pizza dough I just use regular yeast (which I also have in my cupboard at the moment). So I'm wondering if I could just use my regular yeast instead of bakers yeast?
There is certainly a difference between different yeasts. Different kinds of yeast react differently, are "happy" at different temperature ranges, produce different amounts of gas, live for different amounts of time. In my little world, however, it's better to use a yeast that you use commonly and understand than it is to experiment with a different yeast that may not behave the way you expect.
The thing is "baker's yeast" is a generic term. If it called for rapid rise yeast, and all you had was active dry yeast, I'd say to go out and buy some, or your bread would become flat. Chances are, you have one of those two kinds. They both work in most recipes, but each have their peculiarities, and you need to adjust.
I'd give it a shot, and see how it comes out. If your bread ends up "whacky", then try something else.
According to wikipedia, bakers yeast comes in many different types, one of which is active dried yeast, which I think is 'regular' yeast. So to answer your question, no i don't think there is any difference save for the moisture content, and therefore how you might need to use it.
Probably what you have in your cupboard is Baker's yeast. Baker's yeast is a pretty generic term and could refer to instant yeast or active dry yeast. I'm not sure what your recipe is asking for.
There is a brief explanation of types of yeast here: Beauty and the Yeast
I hope this helps.
per SF baking institute: Active dry can be used at 50% of the weight of fresh yeast and instant dry can be used at 40% of the weight of fresh. Based on the recommendation of the yeast manufacturers, most people are under the impression that 33% is the proper conversion for instant yeast. This is true for an industrial process, but 40% is better in the artisan process, when dough temperatures are generally lower
I have found unless specific, receipes use active dry in the US. Instant requires no proofing but I do it anyway, if it bubbles its still alive