This is the plain 'belonging to Freud and his school' sense. It covers his writing, his theory, the treatment he developed, and later work that follows him. It usually stands in front of a noun: Freudian theory, a Freudian reading of a story, Freudian analysis. The word keeps its capital letter, because it is built on a person's name. Saying something is Freudian says where an idea comes from, not whether it is right.

This sense is about a small accident with a big reading put on it. Someone uses the wrong word, or does something odd, and a listener treats the mistake as a window into what that person was really thinking. The most common shape by far is 'a Freudian slip'. It is usually said half as a joke, and it does point the conversation towards private matters, so it lands differently at work than among close friends.