A product refers to information stored in your Listing Mirror account that is used to populate listing data.
Typically this term is used when talking about your product catalog. You can review this article to understand your product catalog better - Product Catalog Overview.
A listing refers to the external listing on your marketplace, the listing can source data directly from the product level to make multi-channel listing easier.
Typically this term is used when talking about the channel-specific edit pages. If you are editing these listings, you are editing your 'market listings'. You can review this article to understand how to edit your market listings - How do I edit a market listing?
Something to consider is that inventory is tied to your product and the order of inventory source for each listing controlled by your integration settings.