Hello Lars,
Hope you're doing well.
When someone uploads a component into the forge, that person has the possibility to upload the component itself and a demo of it (in order to demonstrate how the component works).
Basically, "install" button refers to the installation of the component itself and "install demo" refers to the installation of a demo about how to use the component.
Please be aware that demos depend on the component itself, so you should always install the component itself before installing the demo in order to avoid compilation errors :)
Hope that this helps you!
Kind regards,
Rui Barradas