aCalendar is a user interface to the local calendar storage of your Android phone. That's why all normal calendar apps (like e.g. Samsung calendar app) show the same data (only some apps, like the MS Outlook app provide their own proprietary sync and do not integrate into the Android calendar system).
Under manage calendars you are able to create new calendars:
- local calendars, which are only shown and saved on your Android phone. These calendars should be manually backed up by yourself, as you risk data loss when your device breaks or gets lost. Please see: Using local calendars
- calendars in your Google account
For other cloud calendars (e..g. in Microsoft public, work or school accounts, or CalDav accounts), new calendars need to be created in the cloud service itself. While Google Calendar is best integrated into aCalendar, aCalendar works with any cloud service which is able to sync your data to Android (specifically to the Android calendar storage).
aCalendar itself saves no user data and provides no own synchronization with a cloud service or an own backup solution.
For problems with calendar synchronization please see: Troubleshooting Cloud Synchronization