MailTips, out-of-office messages, and similar features understand that Office365 and onpremises users are part of the same organization.
Delivery reports and multi-mailbox search work with users who are onpremises and those working in ExchangeOnline.
Authenticationheaders are preserved during crosspremises mail flow, so all mail looks and feels like it is internal to the company (for example, recipient names resolve in the global address list).