I expect this varies from country to country. In the UK it is mostly:
- Socket (or plug socket): the connection on the wall that you plug electrical goods into.
- Plug: the bit that you plug into the socket. The one with prongs on the end of a cable, for a lamp, for example.
- Phone charger (or sometimes just charger): what you normally call the plug for charging your phone.
You can also have extension leads which can be plugged into a socket and have their own sockets, to provide access to electricity somewhere else.
You could say outlet, power outlet, and and be understood, but it's not common. I expect this is completely different in the US.