What is the difference between gradient and vector notation?

Answer 1

In the name of God;

It must be mentioned that a vector has two important characteristics; 1- direction and 2- quantity. in other word for identification a vector these two characteristics must be defined. for example when we speak about displacement of a body it must has direction and quantity.

but about gradient, it has a general mean: difference.

Also a specified mean may be defined for it: "any increase or decrease in a vector or scalar field". it is a vector field.