Essay comes from the word "to test", i.e., you're trying out or exploring an idea. A personal statement is just that, a statement which is 'personal', i.e., not what you would find on formal documents such as a c.v. or transcripts. So, a personal statement may be a type of essay, but it's 'purpose' is to explore your person or, rather, to present it to a committee.
Best,
Anka
