Answer :

IwAsSoMeGuY
Yes and no
Area is used to define the size of surface space available on a 2d object, which only ever has 1 face

Surface area is used to define the size of surface space available on a 3d shape, by adding up the area of all the faces of the shape
AL2006

Sure.  If you find the area of a surface,
then the area you have is surface area.

Others will undoubtedly come along and give you a
more complex answer, but I don't think that's necessary.