These words can mean exactly the same thing; to take place. An eclipse will happen today. An eclipse will occur today. Both of them have alternate meanings in addition to that. Occur can also mean to come to mind. A thought occurred to me. Happen can also mean to be experienced by or befall someone. Something bad has happened to me.

They both have the same basic meaning but I would say that "occur" is more formal. Mind you, each verb has its own set of phrasal expressions: Eg. It suddenly occurred to me that I was late for school. It so happens that my birthday falls during the school holidays. In the above sentences, the two words aren't interchangeable. Apologies if this was more than you asked for!

Agree with alancoots. Both words have same meaning