I'll answer based on my philosophy of the difference between Anime and "Cartoons". I choose to define "Cartoons" as "Western Cartoons" (i.e. those common in America, and to a lesser extent in Europe).
As a general rule, (Western) Cartoons were derived from "shorts" that preceded feature films in theaters of the early- to mid-20th century. These shorts, in turn, got their existence from a form of theater known as Vaudeville. Vaudeville usually consisted of a number of diverse short acts meant to entertain the audience. By the time movies became sufficiently popular, Vaudeville was fading as an art form. However, the need for entertaining shorts to accompany newsreels and other theater activities aside from the feature film were seen as adding value (and time, interpreted as value) to the audience's experience.
Watch older (pre-1960) Looney Toons or Tom and Jerry shorts, and you will see the sort of situational, often physical and slapstick, comedies that characterized Vaudeville acts. (It made little sense to have cartoons showing various athletic feats or magic acts sometimes seen in Vaudeville because, hey, the were animated.)
As Western Cartoons also went through their dry spell (around late 1950s through mid 1970s), they still maintained the format, that is, Vaudeville short acts. In most theaters, only Disney films attempted longer format, dramatic stories that de-emphasized, or even eliminated, the Vaudeville characteristics. More on that later.
[Note: there are exceptions to this throughout, particularly in the Bakshi films and other independent efforts of the 60s, 70s, and 80s, but these rarely rose above cult status in recognition and frequently appeared in art house theaters in major cities.]
Even today, many Western Cartoons (the ones that appear, say, on Cartoon Network) still follow this format. There is almost never any history, memory, character development, or reference to a set of "past" conditions that influence current events. [Yes, there are exceptions. Even The Flintstones had some degree of history, but it was very utilitarian and not at all essential to most of the week-to-week plots offered, which were still very much situation-comedy in nature.]
Anime, Japanese animation, is more episodic in nature, deriving its existence from the (frequently Heroic) Epic rather than a situation-comedy setup. As you know, many series are based on stories found in manga and novels, themselves episodic, and recognizing that characters have a past and are set in worlds that themselves have histories.
Now where did a lot of this philosophy come from? My reading of the history suggests early Disney epics were very influential in the artistic lives of Osamu Tezuka and other forefathers of the anime genre. Certainly the tales found in the three major forms of Japanese theater (Kabuki, Noh, and Bunrakyu) are not epic or episodic, but they are of a fundamentally different nature than the drama-less slapstick comedy that often characterized Vaudeville. Freed from this (and freed from a number of other forms that belonged pretty much exclusively to Western 20th Century theater), anime was able to develop, alongside manga, as a more longitudinal art form.
Recently (mostly since the 1990s), more Western Cartoons have started to work on longitudinal storytelling, whether it be Clone Wars or Venture Brothers or Archer or any number of other works. This evolution will bring Western Cartoons closer to anime, and perhaps rather than calling them cartoons we will be able to describe them as animated works, leaving "cartoon" to describe the theatrical shorts that died along with mid-20th century theaters. Sure, it's a semantic argument. But in my opinion, this is what separates the two (and I do see a substantial, but lessening, differentiation).