When you add something on your phone/Google, if you put it in your "Myname's MRSware Appointment" calendar, the default is "Business". If you put it in your private Google calendar, it will default to "Private" in MRSware. You can adjust these defaults by going to the "Go To" -> "MRSware Sync" -> "Edit Subscription" menu in MRSware.
A Private Appointment can only be see by its creator, and anyone directly invited to it via the Attendees tab. A Business Appointment can be seen by anyone in the User's Management chain, as defined in the System Administration Roles and Filters.