Before November 2018, there was a “legacy mode” in Microsoft Teams that allowed Teams users to send messages to Skype users who didn’t have Teams. You’d see a notification like this:
Now, things are different. For an Office 365 tenant, you have the following policy setting options through something called “Coexistance mode.”
Means users who are licensed can use both Skype for Business and Microsoft Teams. There is no inter-app messaging available. Teams chats go through Teams to other Teams users, and Skype chats go to Skype users.
Send a chat to someone in Teams who hasn't used Teams --> goes to email
Send a chat to someone in Teams who has used Teams --> sits in Teams
Send a chat to someone in Skype --> goes to them in Skype if they're available, otherwise email goes in conversation history
Skype for Business only
This mode means users assigned to this policy will get everything routed to them through Skype for Business.
This mode works in tandem with Skype for Business only. If you’re a Teams only user, then your messages from Teams will show up as messages in Teams for other users also in the Teams only configuration. If you send a message in Teams to a Skype for Business only user, they will receive the message in Skype for Business. Likewise if a Skype for Business only user sends a message to a Teams only user, that user will see it within Teams.
You can set the org-wide policy through the Teams Admin Center. Similarly, you can set the policy for individual users also through the Teams Admin Center, or through PowerShell using the Grant-CsTeamsUpgradePolicy cmdlet.