Why does this distinction matter when buying?

An AGV needs its guidance infrastructure installed and updated whenever the route changes. An AMR adapts to a changing layout without that fixed infrastructure, which generally makes it more flexible for facilities where layouts or product runs change over time.

Are they used for the same tasks?

Broadly yes — both move materials around a facility — but an AMR's ability to reroute around obstacles and people makes it better suited to shared spaces with foot traffic or variable layouts.

Do they fall under the same safety standards?

Both AGVs and AMRs are covered by the same industrial standard, ISO 3691-4, which sets safety requirements for driverless industrial trucks generally.