애자 refers to 장애자. As you might already know, both 자 and 인 refer to person. so, 장애자 and 장애인 have almost always same meanings and contexts. However, 애자 is a form of ridicule; you don't want to use it often to your friends and probably never to the disabled people. 고자 refers to an impotent. This. you might not want to say this often to someone you know either.

애자 is slang and refer to the disabled. 장애인 or 장애우 is formal refering to the disabled. 고자 is also slang and translate "A man can't act like a man."