I think I disagree with Cyris' answer.
I would say that "post" refers to a specific employment position that requires one person's labor.
For example, let's look at this sentence:
There are five teaching posts at the school.
This means that there are five employment positions at this school that require a teacher who can do the work. Once they've hired five people, all the posts are filled. They don't need to hire anyone else. If they only have four teachers, there's an available post at the school.
"Occupation" is a general term referring to the type of job one does.
A: What's your occupation?
B: I'm a teacher.
You could also say "I'm a doctor," "I'm a lawyer," "I'm a baseball player," "I'm a painter," etc. Those are all different occupations.
Does that make more sense?