...urface. Plz help I don't understand this difference. Thanks
If you have a definition, you should post it (if its from lectures notes or a book) but a gradient vector can refer to the tangential vector with respect to a particular variable (i.e. one based on the partial derivative of the surface at a particular point).
It's hard to say with certainty without knowing more information.
I think your problem is where you refer to the "gradient vector" of a surface. There is no such thing. Rather, the gradient vector is the gradient of a function. If we have a function f(x,y,z) then the "gradient of f", also written , is the "vector" . Given such a function, the equation f(x,y,z)= constant, could, theoretically, be "solved" for one of the variables in terms of the other two. Since we can then have z= g(x,y), say, that equation defines a surface. Given the equation f(x,y,z)= C, , the gradient vector of the function is a normal vector to the surface at every point.
(In Britain, the term "gradient" can be used to refer to the derivative of a function, which then is the slope of the tangent line. Chiro may be thinking of that situation. Why in the world can't those Brits speak English!)