What is the difference between mathematical model and algebraic model for polynomial function?

They sure sound like the same to me as well.

An algebraic model is clearly refering to developing a polynomial of degree six.
(The degree of the polynomial that would "fit" the seven points would have to be six if they were fairly random and they were not all on a parabola or straight line of any polynomial of a lower degree."Mathematical model" is a new phrase to me.  See if that terminology is in your notes or your textbook.  If "yes", there should be an example of a "mathematical model" so that you would be able to differentiate between the two (assuming, for the moment, there is a difference).