"Anime" is what Japanese call animated cartoons in general, regardless of country of origin. "Anime" is what we westerners call a cartoon that has either originated in Japan, or is visually resembling cartoons originated in Japan but is made elsewhere. For example Technotise: Edit & I is made in Serbia, but people call it "anime" because the style has been influenced by Japanese cartoons.
'Cartoon' is a broad term for comically exaggerating the human features. 'Anime' is a term used to describe a certain look of exaggerating human features. They're both "cartoons" in a sense, one just brings about thoughts of a certain look You improve on both by exploring realistic human proportions, and learning how to distort them slowly
It doesn't really mater if there is a difference between them--when it comes to improving, the basis of improving ANY stylized form of art (be that western cartoon style or anime) is to draw from life and improve your proportions and anatomy. Once you practice that, you'll find drawing in any style much easier!
Anime, while technically referring to animation as a whole, is generally considered the japanese style of animation. Although one could group it as part of the 'cartoon' genre, most people generally wouldn't. At the same time, I personally refuse to refer to anything anime-styled that isn't Japanese like, say, my own works to be exactly that; Anime-styled. I will generally refer to any non-anime styled or non-realistically drawn animation as a cartoon. So, something like Kipper, or Mr Men.
Cartoon is:a sketch or drawing, usually humorous, as in a newspaper or periodical, symbolizing, satirizing, or caricaturing some action, subject, or person of popular interest. andWhile the specific definition has changed over time, modern usage refers to a typically non-realistic or semi-realistic drawing or painting intended for satire, caricature, or humor, or to the artistic style of such works.
The dictionary only tells you how a word is commonly used, not what the thing actually is or the things history. We say anime instead of japanese animation since its more convenient but it's still in the realm of cartooning.
Look at the cartoon description for a moment, how does that not refer to Japanese cartooning?