Distilled water has been boiled into steam and then condensed back into liquid. Think of it as water that went to a spa, sweated out all its impurities, and came back as a cloud. Purified water is a catch-all term for water that’s been stripped of chemicals and contaminants through any number of methods—reverse osmosis, carbon filters, or even UV light zapping the bad stuff dead.
In short: all distilled water is purified, but not all purified water is distilled. It’s like how all squares are rectangles, but not all rectangles are squares—except water doesn’t have corners, so that analogy is a bit damp.