"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!