The primary difference between product markets and factor markets is that

The primary difference between product markets and factor markets is that:

Product markets are markets related to products, goods, tangible finished items.  This is where you'll get your product for sale and where people will buy it.

while

Factor markets are for the factors of production, mostly intangible, like labor, capital and entrepreneurial skills.  This is what you'll use (including raw materials) to make your product.