iOS can already show a note on the Home Screen, so the honest question is why install anything else. The answer is control. A built-in notes widget shows you the note as the system decides to render it: system typography, system background, no way to make Tuesday's grocery list look different from your partner's message. On a Home Screen that already has thirty things competing for attention, a note that looks like everything else stops registering after a day or two.
WidgetNote is built the other way round. The note is the design surface: paper color, font, text color, text size, where the text sits inside the widget, and a slight tilt if you want it to read as a physical scrap of paper rather than another card. That is not decoration for its own sake — a note you can pick out of your Home Screen in peripheral vision is a note that still works in week three.
The second difference is what happens after you write it. WidgetNote notes sync through iCloud and CloudKit, and a note can be shared with another person so their widget updates too. That turns a private reminder into a small shared surface between two phones, which is a different thing from a notes app that happens to have a widget.