The Windows 10 installation media has all the bits and bobs needed for Home or Pro, and it is the license key that determines what will be activated. In fact, the actual Windows 10 Home installation still has all the bits and bobs needed for Pro, it's just that the features specific to Pro are not activated. That's why it's possible to go to Settings, Update & Security, Activation, Update product key then enter a Pro key and after Windows does it's "under the hood gyrations" you then have Windows 10 Pro. There is no reinstallation required.
The Enterprise and Educational editions are their own things and must be sourced from the enterprise or educational institution they're connected with.