Yes, it's somewhat possible. What you're looking for is called a Bridged USB Cable. It's just what you described, with a USB adapter on each end. The big difference is there's a small box of sorts halfway through the cable that tells each PC how to talk to the other. While not common in retail stores, a specialty computer or electronics store will probably have one for around the cost of a standard USB cable.
Though in this case, I don't believe you can connect a laptop or PC to a console and use it as an external HDD. You could certainly connect the two, but unless the console allows you to specify the storage device, it won't work. It's just not designed to do that.
The cable you have is a standard USB cable, and you do -not- want to connect the two with that. USB ports provide a small amount of voltage to power external devices(some of which need more power and have their own power source). By connecting them with this cable, you'll be effectively sending this current to another USB port and possibly burning it out or otherwise damaging it. I tried it once when I was younger and uninformed, and it actually caused a small surge and shut down one of the PCs(thankfully causing no long term damage that time).
The other cables with different ends are commonly known as A/B USB cables. You use them to connect devices to your PC, and they work like standard USB cables. It'll probably have the same effect and won't allow you to connect the two PCs or devices.