Question; when I learned Vector Calculus back in college, I used Marsden & Tromba as our text book where they equate the derivative of a function from R^n->R^m

Question; when I learned Vector Calculus back in college, I used Marsden & Tromba as our text book where they equate the derivative of a function from R^n->R^m with the Jacobian. Is matrix calculus the same thing, just a slightly different notation?