Very interesting, I thought something different too. I thought that Don Gero is the title given to whoever possesses Don Gero's Mask, and that person then conducts the frog choir. So the Goron was Don Gero when he had the mask, and Link became the new Don Gero once the Goron gave him the mask.
But this motivated me to do a little research, and when you get the mask the description reads, "You got Don Gero's Mask. It looks just like Don Gero, conductor of the frog choir!" This doesn't really prove anything 100%, but I'd say this piece of evidence strongly implies that the real Don Gero is a frog and the goron just had a mask that looks like him. Maybe Don Gero the frog is just famous in Termina and the goron is just a fan of his so he wears a mask of his likeness (like how the guard in OOT wanted a Keaton Mask because it was popular in Hyrule). That or what biggreenhawk said about his spirit transforming into a mask when he died.