While cartoons may refer to many forms of media, they are 'animated ...

The Argument
With the idea of cartoons, many first think of television channels like Cartoon Network and Nickelodeon, two leading media channels. However, that's not entirely the case. The first cartoons were illustrations meant for satire. Today people see these in newspapers and comics.
Cartoons actually started out as illustrations before moving on to what people recognize it as today. Going a bit into the history they started as far back as 1754. Their main purpose was to illustrate topics to make them more understandable. Whether political or comedic.[1] Today they can still be seen in newspapers but most people know them by their television counterpart.
Anime directly falls into animation, it's in the name. With cartoons though people might find them a bit harder to relate. Going directly into the first cartoon and anime they aren't too different, it's just how they're presented in the media that makes them seem so.
Tetsuwan Atomu, better known as Astro Boy, was one of Japan's First animations while Enchanted Drawing was one of America's first. 1906 and 1900 respectively. Anime vs cartoon, except they both follow the similar model of being 2D drawing on cells, played at a fast pace to look like actual motion.[2][3]
People might get picky on what you call a show, whether or not it's a cartoon or anime, but at the end of it all they are both animations.
Counter arguments
Animation has existed since prehistoric times, though it may not've been as complicated as CGI animation. It truly took off during the 19th century. Shadow puppets, magic lanterns, they're types of animation, however, not all cartoons are animations, and sometimes things that are cartoons should really be labeled as anime.[4]
In the debate of cartoons and anime people focus almost exclusively on the cartoons that are shown on the tv but those aren't the only cartoons that exist. The question to ask is what constitutes as a cartoon? What truly separates it from everything else? What 'defines' these animations?
Cartoons are defined by their humor. Even if there's an element of seriousness or tragedy, more often then not they focus on the comedic aspects and highlight them in the shows. Anime on the other hand has a higher focus on character relations and bonds. These interactions between characters are almost always the driving point of a plot.
Cartoons and anime are watched for different reasons, and exist for different reasons. While they have their similarities they aren't the same thing.
Proponents
Premises
[P1] While people use different ways to create animations, they are still 'animations'
Rejecting the premises
[PR1] Cartoons are mainly defined by humor while anime is defined by emotion and bonds