What is the 'Chat' function on my Smart Prime 6

I just got my new phone (Vodafone Smart Prime 6) and have a function called 'Chat' when in Message settings. The messages sent on this chat function are shown in green (compared to the blue ones when sending a standard SMS). They also show when somebody is typing and when the message was read. At first, I thought those are Google Hangouts, but I could not find them under the Hangout webpage on https://hangouts.google.com , which led me to the conclusion that those are not Hangout chats. Could you tell me which service this is, and more importantly -> is there any chance to back up those messages (either via textfile export or as a file that can be imported to a new -same model- phone)? I am running Android 5.0.2. You can see a screenshot of that settings menu on the link underneath.