First language is what you are familiarr with.It may be your mother tongue but NEED not be your mother tongue.That is the difference.If my parents are Bengali and I live in Punjab and speak Punjabi from Day one my MT will be Bengali though my First language will be Punjabi.If my parents are Punjabi and I speak Punjabi fluently, then my MT and First language is Punjabi.Hope I have cleared this.Let me close this.
First language/mother tongue, is what a child learns at home from their parents.
You can have more than one mother tongue or native language.