At Ignite we announced a major improvement to the way secure external sharing of files and folders works in both OneDrive and SharePoint in Office 365 and we wanted to share what this means for users...
Organizations that are opted into First Release for all users should now have this feature!
BRETT COX in the OneDrive or SharePoint admin center you have the ability to change external sharing settings. This feature is enabled when your settings allow sharing to new external users.
Rudi Schmitz In your first screenshot (the one with the orange icon) what happens when you click on the "x" ? That should bring up a dialog like the one below. Once you click "Remove link" the link will be deleted and will stop working for people who have it.
The second screenshot is actually showing a direct (or 'canonical') link to the file. If you grab that link you should see it is not the same link as the one you previously created. This direct/canonical link is the same type of link that you get when you share to "people with existing access" (so not really sharing in the sense that the link does not grant any new permissions). We'll look into the wording as I agree it can be confusing that it uses the term "specific people".