Are the median and the mean always the same value?

No, not necessarily. They each measure central tendency but in different ways. The mean measures the average of all of the scores while the mean is the middle score. In a normal distribution the median and mean must be equal. In other data sets, they may or may not be equal.

For example, the set {0, 1, 2, 3, 5, 7, 10} has a mean of 28/7 = 4 and a median of 3.