In addition to what @user721 describes, and just to clarify what is perhaps nomenclature:
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Calendar events are events that show up in the system Calendar app and apply to an entire note only, you set them by clicking the little calendar in the top right corner of the note.
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Reminders are those that show up in the system Reminders app and apply to a single paragraph of text inside the note only. You can set them using the Insert > Reminder menu or using the
\remindertext action as @user721 describes. -
Quick Reminders is the name of the premium feature that allows you to create a reminder that is not linked to a particular paragraph of text. Think about it as a “standalone” reminder, which you can create if you right click a day in the calendar in the inspector. For instance if you remember you need to get milk but don’t want to type that in one of your notes. These reminders show in the inspector but not anywhere in the text.
Most of the time you will want to use either calendar events (for instance to tie a particular note to a certain meeting) or regular reminders that you insert in the text of your notes (for instance to remind you of a particular task you wrote down inside a note).