What is the difference between identity and equation?

An identity is an expresion that is true for any value of the letters:

x + 1 = 2x + 2              (is true for any value of x)
(a+b)·(a+b) = a2 + 2ab + b2            (is true for any value of a and b)

An equation is valid only for a small number of values of the letters:

x + 3 = 5                    (is true only for x = 2)
x2 - 1 = 0                  (is true only for x=1 and x=-1)