How to hide calendar but receive reminder notifications? I have a calendar containing only regularly recuring dates. I would like to hide this calendar or these dates from the ordinary Google calendar app and the Google calendar widget.

The reminder notifications of these dates should not be disabled. 

I activated synchronization in the Google calendar app and deactivated the display calender. Now the dates do are not being displayed, neither in the app nor in the widget, but I either do not receive the reminder notifications.

P.S. What is the difference between those two settings?
The easiest way to achieve this is to install a 3rd party calendar app which uses the Google calendar backend, and tell that app to not show that specific calendar, while leaving it enabled in the default Google calendar app (aCalendar  would be a good and relatively light-weight choice here). As the Google calendar is responsible for the alerts, you still would get them (and the corresponding notifications), while its content wouldn't disturb you working with the 3rd party app. I do something similar, and use the mentioned app, so I really can recommend it.

To the detail question: Synchronization is what the name suggests: updating changes made on either side (for a disabled calendar, obviously only in one direction). It's probably separated from (de)activating a calendar so you can activate it up-to-date even when having no network connection -- just my guess, but that would make sense.