Giving access to sites and content to internal or external users is accomplished via "Sharing". The options for sharing content are dictated by the security settings of a site. By default, all sites/files can be shared internally to other faculty and staff within the UI. Allowing site/file sharing with external users is also an option that can be enabled on a site. The experience of sharing varies depending on who is being shared with (internal or external user) and the type of email address being shared with.
Like most cloud-based services, there are occasional changes to processes/features on Office 365 and the experience of sharing sites and content can vary as Microsoft continues to evolve the platform.
The most current information on Sharing is available at the following Microsoft links: