Usage of "diary" and "calendar"
In British English, a diary is normally a book where you note down appointments and events on particular dates. A calendar is usually hung on the wall, or placed on a desk, and may or may not be used to write appointment on. Diary also means a personal journal.
I understand (and Kristina Lopez confirms) that in the US only the latter is called a diary, and calendar covers the first two meanings.
The calendar in Microsoft, Google etc systems partakes of the nature of both a calendar (UK) and a diary (UK).