The personal statement or statement of purpose
A personal statement usually explains motivation, relevant experience and values. A statement of purpose usually weights research interests, academic preparation, career direction and course fit more heavily. Institutions use the terms inconsistently, so follow the programme's own prompt rather than the label.
What it is assessed on: whether there is a credible line connecting what you have already done, what this programme involves, and what you intend to do next. Strong evidence is specific — a dissertation, a project, a professional problem, a method, a publication, a responsibility that prepared you for this work.
Avoid retelling your CV in prose, praising the institution in language that would fit any institution, or making claims your transcript and references cannot support. Explain gaps or career changes only where they are relevant, and factually. If both a statement and a proposal are required, do not duplicate passages: let the statement explain you and the proposal explain the research.
Oxford's statement guidance distinguishes personal motivation from a research-focused statement of purpose and points applicants back to course-specific criteria.