Microsoft Teams is Microsoft’s new chat application for Education, Government,
Islands Mode is the most basic mode where Skype and Teams have no integration at all, any chat messages you send in Skype will go to the other persons Skype client, and any messages you send in Teams will go to the other persons Teams client. There is also no inter-op for meetings.
Teams Only Mode
Teams only mode makes it seem as if the users will, be able to receive and send messages from Teams to Teams. However this is not the case, Teams only mode actually indicates that the user will outright be able to use the Teams client and that the Skype for Business client no longer has a use. However, chat messages between Skype users and Teams only users will continue to be sent. In other words, if a one user is in Teams the only mode and the other, use Skype then a message sent from the Skype user will still be received by the Teams Only user and vice versa. Meetings, however, are only created for Teams and other users would need to use teams to connect to a meeting.
Skype for Business With Teams
Skype for Business with Teams is kind of what it sounds like. This mode means that any one on one chats will still happen in Skype, however users still get the Collaboration features of Teams. Meetings are only done through Skype.
Skype for Business Only
This mode is exactly what you would think, Microsoft Teams is completely disabled and everything happens through Skype, this is a good mode if you are looking to control what users have access to.
Each mode has a purpose but the way Microsoft has their documentation it could use some real work. However which mode you should choose depends solely on how your business, government or school operates. It may make sense to have the majority of users on Skype only with a pilot program of users in Teams only mode. They would not be able to have meetings but the overall chat functionality would remain. Or you may want to make a full switch to Teams Only or even keep them separate entirely, everything is up to you.