Fermentation occurs only when there is not sufficient oxygen available to permit aerobic reactions. (Note, this isn’t pictured in that overall picture at the top of this post).
Let’s pretend your muscles don’t have enough oxygen to attach these “hot potato” hydrogens onto oxygen. The NAD will then reattach these hydrogens back onto the middle carbon of each pyruvate to create lactic acid. The same way pyruvate is known as pyruvic acid, lactate is also called lactic acid, they are the same thing.
