Is there a possibility to sync 2 calendars within the same account?

I want to have a calendar on a website, lets call the calendar Public.
Public should only show the title of a booking, while my separate one, lets call it Business, I should use to add some more information to the bookings.
Is this possible some how?

I've tried to export and import the Public calendar to Business and then re import it again to Public. But it doesn't work.
The only way I can make it work is to manually enter the bookings from Public into Business.

Please tell me there's another way...