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Republishing a schedule means you have already published it once, made some modifications to it and wish to send it out again. 

In this instance, the option you see is not Publish This Schedule as it was when you first when to publish it.  Every time you make a change to a published schedule you will see Send Changes to Staff.  This means that only the staff who have been affected by the modifications will receive email and/or texts notifying them of the changes.

Note:  You can decide when to send out your changes based on the settings provided in the system.  Under System Setup - Communications two settings are available please see below.