How is long division of polynomials the same as long division of numbers? How is it different?

Well, you are trying to simplify the numbers and the equation. You are trying to get the smallest possible number or solution. A difference between the two is that polynomials have factors and variables. Numbers are just numbers. With a polynomial, you have to combine like terms and try to reduce the length of the equation. You may not always fully solve a polynomial. With numbers, you probably will get an exact numeral answer.