The traditional USB connection has a host with a USB A socket, which provides power; a cable with a USB A plug in one end and a USB B plug in the other end; and a device with a USB B socket. All traditional USB cables are A to B cables, with a USB A plug and a USB B plug; an A to A cable would allow connecting two hosts together, and both would try to provide power at the same time, which might damage the hardware.
USB-C is completely different; all cables have two USB-C plugs, while both hosts and devices have USB-C sockets. Which side provides power is negotiated through a dedicated configuration channel.
USB A is a rectangle, and USB B is closer to a square. I've also never seen anything aside from female USB ports and male/male USB cables (aside from extension cables).
Type C is bi-directional, so can replace either or both plugs.
https://itsolutionindia.files.wordpress.com/2014/08/usb-tuto...
I assume in the first paragraph you mean a usb A cable with plugs on both ends