This is a huge misconception for some people who are not familiar with manga and anime. While certain genres like kodomomuke (for kids), shonen (young boys) and shojo (young girls) are meant for younger audiences, genres like dansei (men), and josei (women) are targeted towards mature audiences.
Since this genre of anime and manga are targeted towards kids, the stories are usually simple and incorporates moral values to teach children to be well-behaved and considerate towards others. Notable examples include Hello Kitty, Doraemon, and Chibi Marukochan.
This seems like the most popular genre as chances are, most of the popular manga and anime you have heard of are of the shonen genre. Shonen mangas and animes are typically action-based and the protagonist is usually a male. Harem plots and sexual fanservice are also common. Even if romance is present in the manga, it is usually not intense. An example being Dragon Ball where there is not much romance between Goku and Chi Chi or Bulma and Vegeta. They just get married… out of nowhere. Other examples of shonen manga and anime are Attack on Titan, Death Note, One Piece, Naruto, Bleach, Detective Conan and Slam Dunk.
Contrary to shonen, shojo plots usually revolve around a female protagonist and romance. Reverse harem is a common feature, along with homosexual relationships such as yaoi (boys’ love) and yuri (girls’ love). Popular shojo manga or animes include Sailor Moon, Fushigi Yuugi, NANA, Revolutionary Girl Utena and Full Moon o Sagashite.
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Dansei genre is usually more serious and can be darker and more violent than the shonen genre. The art style is also usually more realistic such as smaller eyes instead of the big, dolly eyes typical of genres meant for younger audiences. It also commonly features an older protagonist. While shonen commonly dwells on the good versus evil plot where the good usually wins, dansei can be more cynical and explores more on the grey areas. Famous examples of dansei are Akira, Ghost in the Shell, Berserk, and Mushishi.
Like shojo, josei mainly focuses on romance but a more realistic one. It might also contain mature sexual content and subjects like rape and adultery. There are not many josei animes due to many josei mangas not being as popular as other genres. Examples of josei titles include Paradise Kiss, Loveless, Makai Oji: Devils and Realist, Honey and Clover, and 07-Ghost.
These are just meant as a general guideline and many people read mangas and watch animes which are not targeted to their gender and/or age group. You can certainly be 40 years old and watching Doraemon!