Did Hector and Ernesto tour with the same type of guitar?

It's well-known in Miguel's town that Ernesto de la Cruz had the distinctive guitar with the headstock looking like a skull (from his mausoleum) but did Hector have the exact same kind, as owned by Miguel but him thinking it was de la Cruz's? If they were the same, I could see how Miguel would think that.

It was the only thing I was confused about, that Miguel should be so convinced that the famous Ernesto de la Cruz was his relative, but the only explanation would be that his guitar (which gets destroyed) is the same as the one in de la Cruz's mausoleum and that Hector (Miguel's actual relative) would tour with Ernesto, performing with them.

Am I correct?