Answer :

surface area is the combined areas of all the sides of the shape and volume is the area within the shape

for example if you had a box filled with water the area of the box is the surface area and the amount of water would represent the volume
Surface area is a quantity of measurement associated with 2 dimensional shapes.
Example:  Area of Rectangle = Length * breadth
                   Area of triangle      = (1/2) * base* height.
While:
Volume is a quantity of measurement associated with 3 dimensional solid shapes.
Example:  Volume of Cuboid = Length * breadth * height
                   Volume of sphere      = (4/3) * Pi* r^3.

We can see that Area is 2 dimensional while volume is 3 dimensional.