Advanced messages (or Enhanced messaging) use a new messaging technology called RCS and these messages are different from the normal SMS and MMS messages.

You can check if you are using RCS in your messaging app by long pressing on a message (that was not backed up) and select Show Details, if it says “Advanced Message”, “Chat” or “Rich Communication Services” then this is an advanced message (called RCS), it’s not an SMS or MMS message. 

Google’s Messages app supports RCS messaging with most mobile service providers in the world. Messages stores these messages in the SMS/MMS database on the phone as MMS messages and SMS Backup & Restore can backup and restore these messages. 

UPDATE Starting with v10.15.002, SMS Backup & Restore supports backup of RCS/Chat messages on Samsung phones (using Samsung’s Messages app). These messages get backed up as normal SMS/MMS messages depending on the content and will be restored as normal SMS/MMS messages. 

Note that since these messages do not get restored back as RCS/Chat messages, this may result in duplicates appearing in the Samsung Messages if a restore is performed with existing RCS/Chat messages already in the Samsung’s Messages app. To work around duplicates, you may need to delete the messages from the Samsung’s Messages app, or use a different messaging app like Google Messages.