What is the difference between real numbers and integers?

A basic answer that is not technically complete but correct as far as it goes: The integers are the natural numbers including 0; 0, 1, 2, 3, 4... along with their negatives. All the numbers in the set {....-3, -2, -1, 0, +1, +2, +3....}. The real numbers are all the numbers, rational and irrational, that can be represented as points along the number line, including numbers that have repeating or infinitely long non-repeating decimal components.