There's a decent presentation here that basically goes over what you're asking.
As an inhibitor, azides are similar to cyanide in that they inhibit complex IV by binding cytochrome oxidase, resulting in a sort of chemical asphyxiation.
Uncouplers are a little harder to wrap your head around. They embed in the membrane space, and we know that ETC and proton pumping depends on the established proton gradient across a membrane. Uncouplers _uncouple_ the proton gradient from the electron transport chain, allowing protons to diffuse across the membrane, effectively negating the proton gradient.