“Quantify” is ” the mathematical operation” and “quantitate” is “counting the numbers”.
They are listed as synonyms, but that is the difference between them according to one professor of Physics. (Physicists apparently use the terms a lot)
Quantitative: -adjective 1.that is or may be estimated by quantity.
Quantitive: Estimable according to quantity; quantitative."
Basically, they are the same. Quantitative is probably more commonly used.