The phrase "first difference" is usually associated with a sequence of numbers: a(1), a(2), a(3), a(4), ... . The sequence may have a simple rule for generating the numbers , a complicated rule or, if it is a random sequence, no rule at all.The sequence of first differences is a(2)-a(1), a(3)-a(2), a(4)-a(3), ...
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Difference means the answer of a subtraction equation, such as 4-2=2. 2, the answer to the equation is the difference. First difference may mean the first answer to a multi part equation.