Explain the Difference Between a Will, a Lasting Power of Attorney, and Probate

Everyone knows they should have a will. Almost nobody knows what an LPA does or why probate is not the same thing as a will being read out. This explains all three: what each one is and when it matters, the single thing it does that the others cannot, and what happens if there is no will. Plain English, UK context.

Explain the three legal concepts of a will, a lasting power of attorney, and probate in plain English:
(1) What each one is and what it does; (2) when each one becomes relevant in a person's life; (3) the single most important thing each document does that the others cannot; (4) what happens if a person has no will when they die.

Keep each explanation to one short paragraph. Use UK legal context. If any of the three requires a specialist to set up correctly, say so plainly.