According to Bread World, baker's yeast comes from the same species as brewer's yeast (Saccharomyces cerevisiae) but a different strain. Because yeast multiplies so readily, the manufacturing process is simple.
A single yeast cell is chosen, separated from the rest of a healthy culture, and placed into a petri dish or test tube for cultivation. This dish or tube contains nutrients, often including sugar or molasses, which prompt growth. The yeast multiplies and is finally moved into a fermentation tank, where it multiplies over many generations until harvest. This results in pure yeast, ready to be separated from the culture and used in baking.