The short answer is that the names are used loosely. One program’s “personal statement” is another program’s “statement of purpose”, and some programs use both names for the same document on the same page. So the first rule is simple: read the program’s own prompt, and answer that, whatever it is called.
Still, when the two names are used carefully, they usually mean different things, and it helps to know the difference.
The statement of purpose
A statement of purpose is about your academic and professional direction. It answers three questions: what you have done that prepares you, what you want to study and why, and what you will do with the degree. It looks forward. Its evidence is your work, research, projects and training, and its center of gravity is the program: why this one, and what you will do in it.
The personal statement
A personal statement, used in this narrower sense, is about you as a person: the experiences and circumstances that shaped you, a challenge you met, the perspective you would bring to the program. It may cover ground a statement of purpose leaves out, such as your background, your community, or what made you want to pursue this field in the first place.
The line between them is not sharp. A good statement of purpose has a person in it, and a good personal statement still shows what you can do. The difference is emphasis.
When a program asks for both
Treat them as two halves of one picture, not two attempts at the same essay. Let the statement of purpose carry your academic plan: preparation, goals, fit. Let the personal statement carry what the plan leaves out: where you come from, what you have had to overcome, what you will add to the people around you. They should agree with each other, and they should not repeat each other. If a story appears in both, it should do a different job in each.
When the prompt is unclear
Some prompts only say “Please submit a statement.” In that case, write a statement of purpose that answers the three questions above, with enough of yourself in it that a reader meets a person and not a résumé. Check the program’s frequently asked questions and any guidance for applicants, and if you are still unsure, ask the admissions office. It is a normal question, and they would rather answer it than read an essay that misses the point.
What does not change
Whatever the document is called, the same things make it work: real evidence early, a direction concrete enough to picture, and a clear reason this program sits between the two. The personal statement guide walks through all of it, step by step.