If I have a license/subscription for Document Creator on Business Central (online/SaaS), can I use my license for an on-premise installation as well? And the other way around?

You can not use your Document Creator license/subscription that is linked to a Business Central online/SaaS environment, for a Business Central on-premise production installation.

You can also not use your Document Creator license that is linked to a Business Central on-premise production installation, for a Business Central online/SaaS environment.

The Document Creator license for a Business Central on-premise installation is linked to the Serial No. of your Business Central license (BC Serial No. a.k.a. VOICE ID a.k.a. PSBCID).
The Document Creator license for a Business Central online installation is linked to the ID of your Azure Active Directory (AAD) tenant).

However, you are allowed to use your Document Creator license for development and testing scenarios.