Things that happened long ago occurred a very long time in the past. Your grandfather might refer to his long ago childhood, for example.
Things that occurred in the distant past transpired long ago, and you'll often hear this term when people talk about history or tell fairy tales. Your social studies teacher might say, for example, "Long ago, marriage was a financial transaction between two families," or you might read a fable that begins, "A beautiful princess lived in a castle long ago..."