You've got some good answers already.
Ale - Typically fermented warmer, 60F-70F sometimes above for specific varieties.
Lager - Typically fermented colder 40F-55F
But to clear something up all yeast ferments more aggressively the hotter it gets, right up until the temp kills it Somewhere around 110F. The varieties of yeast selected for specific type of beer has to do with the flavor profile it produces at certain temperatures and/or how low a temperature it will still remain active at. Lager yeast will remain active in the 40s but most ale yeast will go dormant as you drop into the mid 50s. However, lager yeast still becomes slow to ferment at the low temps lagers are typically fermented at. So as a brewer you must add (pitch) more yeast for a lager than you would for a similar ale and you must also allow for a longer fermentation period. In addition to taking longer to ferment lager yeast is also slower to fall to the bottom once fermentation is complete so following fermentation there is a "lagering" period that is needed to clear the beer, otherwise it would be cloudy. Lager is a German word meaning "to store" and is used because before refrigeration lager beers would be stored for several months in caves that stayed at a consistently low temp.
Lagers are typically known for their clean flavor profile. That could be considered good or bad, depending on your taste. That's because generally the colder the fermentation temperature the fewer byproducts a yeast produces. In ales, however, some of those byproduct flavors are desirable. They can be flowery, fruity, clove, anise, banana, buttered popcorn. Hefeweizens often have a slight clove and sometimes noticeable banana flavor. In that style those flavors are preferred. In most other styles they are not preferred and are usually considered a flaw.
A lager yeast fermented at an ale yeast temperature would produce way more off flavors than the ale yeast would. An ale yeast fermented at lager yeast temps would not fully ferment the wort and there would be a lot of left over sugars in the beer resulting in syrupy-sweet beer and less alcohol than was intended.
Most, but not all, stouts are ales. They are made in mostly the same way that a pale ale would be made only roasted malts are used which changes the color and adds coffee like or sometimes chocolate like flavors.
Interesting fact: Guinness Stout is often considered to be a strong beer, but the alcohol content is around 4%abv and it has about as many calories as a Bud Light. Color is not everything when it comes to beer.