I agree. Consumption v. production is a good way of looking at it.

Note that this definition means that certain pieces of software could be considered either "sites" or "apps", depending on how they're being used.

For instance, blog software like Wordpress would be a "site" for the readers, but an "app" for the person who writes the posts.

A "product" can consist of different parts.

One part is an editing software/gui and one part is a reading software/gui. Both working on the same data.

Since both are used by different kind of users, I would design them as different programs (one a site and one an app).