A hybrid mobile app usually refers to an application built using a combination of web and native technology that is distributed via a native app store. These apps go through Apple, Google, Microsoft, etc’s app store review process.
A Progressive Web App is an application built using web technology that runs in the browser and may be added to the home screen. They do not need to be distributed via native app stores, but can be included in them. Microsoft includes PWAs in its Microsoft Store as of 2018 and Trusted Web Activities make it easier to submit PWAs to the Google Play Store.
Some hybrid mobile app platforms include PhoneGap (aka Cordova), Appcelerator Titanium, and Ionic. You don’t need a platform to create a hybrid app, but they are helpful because they’ve already taken care of creating a bridge between native APIs and JavaScript APIs.
Progressive Web Apps simply run in the browser so they can be built with basic HTML, CSS and JavaScript.