Let's see how bad this goes, if it goes bad.

Anyone feel like disagreeing with the topic title?

and GTA is an RPG!

Zelda is an FPS!!!

I guess everyone has there opinion. Although I'm not sure if you actually believe that based on what you typed into the OP.

Yes, animes are cartoons.

Still, we make a difference because the style is different. It's not made the same way, it's a different culture, sometimes not the same public (not many western cartoons for the 18-25 )

I think Anime in general is aimed at a more mature audience than Cartoons. That could just be me though.

According to Wiki a cartoon is: "A form of two-dimensional illustrated visual art. While 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.".

If we go by this definition, some animes can indeed be considered cartoons. 

I see it more Western vs. Eastern Animation
Tho both have mixed them before.

Depends on your definition of mature. Most animes nowadays involved either extreme violence or fan service, that imo, isn't mature. 

I've always felt like what really separates anime and cartoon is how the story is treated.

Example: Spongebob I feel safe to say is a cartoon
Avatar: The Last Airbender I do not.

Hunter x Hunter I feel safe to say is an anime
Gintama I do not

Most cartoons also use different means of expressing their emotions. Anime use more symbolic expressions while cartoons use more literal ones, it seems.