What is the difference between deviation and standard deviation? In my textbook, it describes the standard deviation "as a number that measures how far data values are from their mean". On the other hand, it says this about deviation: "if x is a number, then the difference "x- mean" is called the deviation". Are they the same or are they different from each other?

Deviation, is as you said, how far a single number is from the  mean.
However, a standard deviation (describing a set of numbers) is the "root-mean-square" of the deviations. So the standard deviation is basically like the average deviation of the whole sample from the mean. 
