Difference between Messages and Messenger apps

The native Messages app is preloaded with iOS and is what is used for iMessage, and can also be used for SMS if you have an iPhone you can associate with the iPad. Message apps you find in the App Store are ones that app developers sell for other message services. I'm not exactly sure what you are referring to when you say "the Messaging app".

Yes, I believe the blue one is Facebook's Messenger. The Messages app for the iPad has a green icon. Facebook's Messenger app is to send Facebook messages in their system.