Hi, Adam, and welcome to Apple Discussions. Your post sure does sound strange, but that may only be a product of the way you're describing what you see. Can you identify a particular downloadable file that has behaved this way for you, so I can have a look and download it for myself?
My suspicion is that you're downloading .dmg files, which are disk images. [Read about disk image file formats
here.] When you double-click a .dmg file's icon, the file is decompressed into a "virtual disk" that is mounted on your desktop. Double-clicking the icon of that "disk" shows you its contents, just as if it were a floppy disk, CD, hard drive or flash drive. What is really throwing you, however, is the fact that the real disk space occupied by those files on the virtual disk is always on your startup volume, not some other volume such as your external drive. This is true even if the original .dmg file resides on another volume. As the .dmg is expanded, its decompressed contents are written to the startup volume, not to the volume where the .dmg is located.
You can free up that space on your internal drive by "ejecting" the virtual disks that appear on your desktop. And you can then free it up on the external drive by trashing the .dmg files and emptying the Trash. If you try to trash the .dmgs while the virtual disks are still mounted on the desktop, you'll be told they are in use and can't be trashed. You must "eject" the virtual disks first.