‘Kindle’ always requires some qualifying terms applied to it. I prefer to use what Amazon uses on their support pages, e.g.:
https://www.amazon.com/gp/help/custo...deId=201263790
I think the ‘generation’ naming is somewhat post hoc but they have been pretty consistent about it for awhile. Yes it is more letters to type but generation number tells a little more, such as when it was released (roughly number of years since first gen) as well as what software is running on it (current update supports 6th generation or later).