What is the difference between normal and perpendicular? What is the difference when a line is said to be normal to another and a line is said to be perpendicular to other?
 A: There is no difference between saying two lines are perpendicular and that one line is normal to another line. It is literally a synonymous term, like saying that you take the product of two numbers or you multiply two numbers.
A: There are different kind of contexts you use term normal in mathematics. You often use perpendicular in case of two or three dimensional geometry, and in hi-dimensional spaces (e.g. infinite-dimensional) a term orthogonal is more common. On the other hand in the context of vectors, normal usually means also that the vector is of unit length, however this is not a must (but it is for example if you speak about orthonormal base). 
There is yet another related meaning in computer graphics, where normal is the direction which you would use to reflect the light. This can be a vector perpendicular to rendered face, but for nice effects you use one perpendicular to the original surface, not its approximation. Also, there is bump mapping technique that lets you change the normal vectors and achieve look of some kind of wrinkles and bumps.
Finally, e.g. in topology or group theory term normal means something completely different, however, I will leave those and others out as I suspect this was not the scope of your question. Hope this helps ;-)
A: Even I agree to the above contexts. Normal is more relevant to 3-D(Line and Surface) and perpendicular to 2-D(Line and Line = One Plane). 
This is correct when we do say normal to surface and perpendicular to the line.
A: Normal is 90 degree to a surface but perpendicular is 90 degree to a line
A: If normal is 90 degree to the surface, that means normal is used in 3D. Perpendicular in that case is more in 2D referring two same entities (line-line) with 90 degree angle between them. Normal in this case could refer 2 different entities (line-surface) making this term valid for 3D case (I definitely remember hearing term "line normal to surface", rather then "line perpendicular to the surface") - line and surface makes 3D case; line and line is one plane - 2D. This I just figured out from one of the answers here which made most sense for me.
A: A normal is an object such as a line or vector that is perpendicular to a given object. For example, in the two-dimensional case, the normal line to a curve at a given point is the line perpendicular to the tangent line to the curve at the point.
