What is the difference between normal and perpendicular?

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 ;-)

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.