This distinction trips people up on exams and in real projects. Get it clear once, and it stops being confusing.
Philosophy = a set of values and beliefs. Agile is a philosophy.
"The term agile refers to a mindset or way of thinking about work. Agile is not a specific set of practices or techniques." — IIBA Agile Extension
Agile tells you to value responding to change over following a plan. It does not tell you what to do Monday morning.
Framework = structure without prescribing every detail. Scrum is a framework. It gives you roles (PO, SM, Developers), events (Sprint, Planning, Review, Retro, Daily), and artifacts (Product Backlog, Sprint Backlog, Increment). But how exactly you run refinement or what your definition of done looks like — that's up to the team.
SAFe, LeSS, and DAD are also frameworks, each operating at larger scale and with more prescription than Scrum alone.
Methodology = a complete, step-by-step approach. PRINCE2 is a methodology. It tells you exactly what to produce at each stage and who approves it.
Why does this matter for exams? Because the Scrum Guide explicitly calls Scrum a lightweight framework, not a methodology. PSPO and PSM questions regularly test whether candidates know the difference — and whether they understand that a framework's power comes from not over-prescribing.
Exam tip: "Scrum is a methodology" is a wrong answer. So is "Agile tells you what to do." Both are common exam distractors.