Mainkly where they are placed by the theme.
The main description is at the bottom pf the product page under all the price and add to cart stuff – that means you can put as much information in it as you like – photos, videos, instructions, full technical details etc
The short description is usually put after the price at the top of the page – useful for a quick summery of the product or, like we do, to add a size chart for clothing etc.
Some themes will also let you put the short description under the product in the category pages – or one I saw had the option to have it show when you hovered over the product image in the category page.