How does an external hard drive work?

I recently installed Windows on my Mac, because of course the two systems have to share the space, I have very little space on Windows.

So my question is whether an external hard drive, when connected, provides the laptop with more storage space or whether it works more or less like a USB stick on which I can load things that are not on the laptop.

The second is correct - like a stick.

The exception would be if you put the swap file on the external hard drive, for example. Then, however, the disk must always be plugged in when Windows is running, i.e. Even when it starts up.

Alright thanks.

Is there any other way to expand storage space or do I have to live with it forever?