성인 and 어른 basically are the same, meaning 'a grown-up', 'an adult', but we also distinguish one from the other in the usage depending on the context.
이제 어른이 되었으니까 네 일은 스스로 결정해야 해. In this sentence, 어른 and 성인 are interchangeable, meaning a person who has reached the age when they are legally responsible for their actions.
어른을 공경해야 한다.
어른에게 자리를 양보해라.
Here, in these sentences 어른 means 'the elderly'. We don't use 성인 in this context.
성인영화 refers to the movies which contain sexual scenes, pretty much erotic movies.
그는 어른스럽지 못하다 means that he is an adult, but doesn't act his age.
Hope this helps.