Basically convertible notes were kind of a financial hack that let you take money without setting a price by calling it "debt," even though no one really regarded it as debt. That brought along a couple small negative side effects, but the good outweighed the bad and let you close rounds quickly without $10-25k in legal fees and seemingly endless negotiation.

A SAFE is the same thing, but it jumps through the hoops necessary to not be called "debt" and gets rid of those side effects.