I completely understand the confusion, but "Progressive Web App" or PWA[1], coined by Alex Russell and Frances Berriman[2], has become a specific term for websites that work normally on a pc but can also take advantage of things like push notifications and be installed on the home screen of a phone. You can see a measurable uptick on Google Trends after this blogpost [3].

[1] https://en.wikipedia.org/wiki/Progressive_web_app

[2] https://infrequently.org/2015/06/progressive-apps-escaping-t...

[3] https://trends.google.com/trends/explore?q=%2Fg%2F11bzxympx6...

If anyone wishes to remember what that looked like.

https://web.archive.org/web/20071012231544/http://www.apple....

https://web.archive.org/web/20071012025941/http://www.apple....