Do multiple and product mean the same thing?

No, multiple and product don't mean the same thing. You get the product when you multiply two or more numbers together. e.g. the product of 5 and 7 is 5x7=35. The product of 2, 3 and 5 is 2x3x5=30

Multiples form an infinite set. e.g. multiples of 5 are 0, 5, 10, 15, 20, 25… Multiples of 7 are 0, 7, 14, 21, 28...