However, you can top crop or harvest from the bottom of either type. And furthermore, some historical beers were made with wild yeasts or hybrids of S. cerevisiae ans S. pastorianus and may have fallen into either category.
But they are all harvested at the bottom unless you’re doing something pretty unusual. And brewers do all sorts of unusual things!
In some circles, even among brewers and even in some brewing literature I’ve encountered, the ale/lager distinction uses the terms ale/beer (where “beer” is the term specifically for lager). And the introduction of hops may not have necessarily made this specific terminology distinction, but it did contrast what we now commonly call beer from earlier (gruit) ales which were brewed with any number of different herbs. Hops, like those other herbs, were added for their preservative qualities. But hops are now generally considered an essential ingredient in beer, ale or lager, and most people would find unhopped beer brewed with other herbs rather odd (at the very least).
If someone says "would you like a beer?" and then offered be a pale ale, a lager or a bitter I wouldn't feel I'd been decieved. They are all beers.
If someone says "would you like an ale?" then the ony one that wouldn't quite fit would be the lager.