Shounen is often tailored to teenage boys. Generally its more about action, adventure, growing up, coming of age and fanservice that doesn't serve a plot. Its an Action Story that can also have themes, with a side of censored boobs.
Mature explores more real world concepts that appeals to slightly older teens but is kinda the middle ground between adult and shounen. Generally more plot-focused, exploring very abstract themes and often being darker than regular shonen. Often not fanservice-y in the same way shonen is because its often just straight up sex and nudity. They are usually darker, more character driven stories with full nudity and sex scenes.
Adult - porn. the sex is a pretty big focus if not the only thing being focused on and is portrayed down to the nitty gritty. While mature does have sex, its portrayed more tamely. Censoring, clever shots, implicated sex scenes. Adult is just porn all the way. It can have a story and themes, but its rare, and often when people talk about "Adult Media' they mean something blatantly pornographic.
Game of Thrones, for example, is Mature, but not pornographic. There are nudity and sex scenes, but you don't see everything that happens down to the nitty-gritty.
Adult is literally any porn.
Shonen is just Shoujo but for boys. XD hope this helps!
