If a website has a public facing front that consumes an API, and there's also a backend for users with more powerful roles that also consumes an API, should both parts of the site use the same API or different APIs (eg: /api/v1/resourceName vs /api/admin/resourceName)?
This really depends on your situation. If your private endpoints absolutely must remain private, then separate APIs is the only absolute solution. In general, that seems like overkill. For most situations, I would suggest maintaining a single API and designing your private endpoints with security in mind from the beginning.
Separate API's
The Same API