I have to disagree on the premise that western comics and cartoons are for kids. Yes generally there are more cartoons target towards children over in the west but the same could be said for japan, the big difference is in animation style and content . Japan produces far more animation so they have a wider range of topics on display while the west seems sort of geared towards comedy when it comes to adult style animation ( Ricky&Morty, south park, Futurama, ect.).
Now getting on to the real topic of Manga vs Comics, this is a big pet peeve of mine honestly. I see people boil the idea of western comics to "superheros" and then write off superhero comics themselves as for children. That is like saying manga only has shounen style stories like beyblade and thats it. Obviously that is a ignorant statement, when applied to manga and comics.
The truth is that western comics have been around longer than the modern superhero, and the superhero was never intended for children and only really got that representation in the silver age when content was restricted due to the backlash from Mothers. The superhero Comic genre is incredibly mature and has been for DECADES. And even during the height of the superhero genre there were thousands of other type of comics, with monster and sci-fi being some of the most popular.
But even if we say for the sake of argument that superheros are intended for children ( although if anyone keeps up with them knows they are not) it is by FAR not the only genre. You literally have the same amount of genres as you would in any other medium.
Here are just a few really good western comics off the top of my head:
East of West- A Sci-fi, Occult, supernatural, Western in a alternate reality America.
Chew- A crime drama, Comedy, about a man who can see the entire past of anything he eats (yes even people)
Black science- A Sci-fi fantasy, action thriller,about a group of scientists hopping through alternate dimensions after their portal device goes awry.
Pretty Deadly-a Supernatural Western about the daughter of death and her journey to kill her father.
The amount of mature and unique themes you can find in western style comics(and comics around the world) is remarkable and shouldn't be regulated to a Japanese Thing. Which seems to be the common misconception.
And so to end this before I find more stuff to talk about, I have to say that both "Comics" and "Manga" are the same thing in my mind . But since language's purpose is to communicate ideas, if the distinction helps you I say go for it.