Outlet one hot wire, one not

The very fact that you separated them for testing is why one is not hot.

Circuits (coming off a breaker) power more than one outlet.

Hot and neutral enter the box on one cable. To get to the next outlet, they exit the box on another cable. Each wire has a black and white, and in most cases black=hot.

If you disconnet the two wires from each other, one will be connected to the breaker. The other will be disconnected from the breaker because you disconnected it.

It's common to use a receptacle itself as a splicing point. The recep has 2 screws that are connected to each other *and to the socket slots). The 2 screws can be used to splice 2 wires to each other (and the socket slots of course).

This doesn't always work, receptacles have "tabs".

If you don't like the idea of using a receptacle as a splice, then look up "pigtailing".