Sidebar, breadcrumb, and tabs are kinds of navigation, like street signs. Users read them to reach certain parts of your application and to determine where they are right now.
That's why I cannot imagine any good reason to have different terms in these places (but surely there are bad reasons, e.g., "different teams designed/implemented it"). Please add reasons you would consider valid to choose different terms.
If one page shows the user's own events, it could be labelled "My Events" instead of just "Events", but I don't see why it should be reachable by a navigation item that is called "Events". If you use "Events" to navigate to the "My Events" page, you mislead users who are looking for other people's events or public events.
If you have an "Events" page without using it as a title (because the top element are the tabs "My Events" and "Shared Events"), I guess this is understandable. [UPDATED UPDATE: I would consider this only for mobile devices, where there are severe space restrictions. Always use a full page header on a desktop page.]
It would be less understandable if the navigation uses "Calendar". If you cannot find very similar terms for the tabs, add a page title.
Alternatively, if there are not too many navigation entries already, you can put "My Events" and "Shared Events" into the navigation.