I think we are saying the same thing, in different words.

I NEVER, EVER said that all beer would be called ale. I am not sure where that came from.

I would not call a keg lager an ale. I would call a keg ale an ale, I would call a keg lager a lager.

All ales are beers, but not all beers are ales.

All lagers are beers, but not all beer is lager.

Ale and lager are beers.