..and the iPhone that killed it.
This idea of the consumer electronics leader, that Sony was in the 80s with the Walkman etc, inspired Jobs long before he founded NeXT. Apple was "Apple Inc." instead of "Apple Computer Inc." in Steve's head for a very long time.
I think they would be more accurate being referred to as iPod and iPhone Generation. The vast majority of people today only came to know Apple ( and Mac ) only after using those products.