I don't think that's the right question that should be asked.
The question that should be asked is "Is anime something different than cartoons or are they cartoons too?"
And this will probably cause folks to have torches and pitchforks aimed in my direction. I don't care because I have logic on my side.
Anime IS cartoons just like manga IS comics.
It's the same thing, and the one thing I got from this video is that in Japan, anime is just the overall term for cartoons, and I completely agree with that.
In this country, however, if something has certain tropes synonymous with Japanese animation, including a certain visual style or a more serious tone in storytelling, some folks consider it "anime."
Purists (I'd never use the "W-word" around here because that's just damned rude) will insist that if it's made in Japan with no foreign/Western production company backing or touching it in any way, it's anime.
One notable example is IGPX was conceived and created by Sean Akins and Jason DeMarco, a pair of producers working for Cartoon Network. Character design, stories, and the series was fleshed out more at Production IG, one of the premiere anime houses in Japan. The style, story, and feel of the series is on par with many of the studio's other works, including Ghost in the Shell: Stand Alone Complex, Morbito, and Attack on Titan, but there are some who say it's not "anime."
If purists are going to use "100% produced/created by Japanese talents and companies in Japan" as a criteria for what's "anime," then a lot of shows folks call "anime" wouldn't be "anime." Most productions are either made in South Korea and China while others are co-produced by French, Canadian, and American investors. These investors are "saving" the Japanese animation industry, and that's a good thing.
Still, we in the States treat this "anime" title as some kind of prestige mark. Something that's supposed to represent a higher quality in animation that's "made in Japan." Purists cringe when folks like me call their precious "anime" "cartoons," even though that's what they are in the end. They feel that's an insult because "anime" is better than "cartoons."
I've seen a lot of Japanese animation over the decades. There are a handful that are very good, a few that are watchable, but a huge chunk of it is unwatchable garbage. Same thing with animation from every country under the sun. It's not that Japanese animation is that much better than American animation or French animation or Canadian animation or Korean animation. We just made "anime" a general "super quality production" label here in the States instead of it being another term for what the Japanese intended the word to mean: cartoons.
Honestly, I feel the closest American term we have to "anime" is "Disney" and "Pixar." We're so quick to call any well-made animated production a "Disney film" or a "Pixar film" even if they aren't made by Disney or Pixar.
It's weird, but until animation fans realize how great animation around the planet really is and they stop putting Japanese productions on a pedestal, the "anime" term isn't going away.