aCalendar is not involved in calendar synchronization. The app is just an user interface to the Android calendar storage and does not save any calendar data itself.
All normal Android calendar apps (such as the Samsung Calendar app) display the same calendar data. Only some apps, like the MS Outlook app, offer their own proprietary syncing and do not integrate with the Android calendar system.
For issues with synchronization please see: General Sync Issues / Sync of two devices
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, 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).