Note-making apps are typically for digital screens, with a limited set of tools for document creation.
Word processors cater both for digital screens and print media. They'd have a richer tool-set and are for power document making people.
Interestingly both categories have made lots of improvements recently, when it comes to sharing, reviewing and co-editing.
Take, Zoho Writer (https://www.zoho.com/writer/) for example. The product beautifully carries the ease-of-use of simpler apps, without compromising on the richer word processor features. This takes the game one-level up. Simple writing apps now have to bring in more document creation features to compete in the market with word processors. Otherwise, they are just their own category with their own market.