What makes a lager yeast different from an ale yeast specifically is the fact that it can metabolize a specific something that an ale yeast cannot. The fact that they give off fewer esters and generally work at a significantly different temperature is true, but not important for the difference in classification.
Now, a Lager needs to ferment at a lower temperature, generally 45-55 ish or so. It varies a bit between strains just like it does for Ales, which require 58-70ish. Lagers were bred to be good at those temps and they do produce fewer flavors compounds in general if kept at proper temps, however some ale strains also exhibit a fairly clean taste profile if fermented low in their range and lagered (aged at cool temps) for a period of time.
So there is some overlap, and for descriptions on what flavors you can get form what, it really depends on the particular strain and the pitching rate and temperature and temperature fluctuations, etc. It's pretty complex with a few variables to consider, so there really isn't an easy answer. In addition to that, different grain bills and hop schedules can influence what the yeast produce in the final product (which can also change over time too...)
But, if you were brewing, say, a SMaSH (Single Malt and Single Hop) beer and had the same wort and fermented both with proper amounts of yeast at the proper consistent temperature, the only difference being one was a lager and the other an ale, then the difference would be the ale (in general) would give more fruity esters, while the lager would be crisper and cleaner, allowing the hops and grain to show a bit more.
But again, it can be hard to tell depending on the particulars. A good clean ale yeast, fermented to be as clean as possible, might come close to most lager ferments in flavor.
