Cordova can wrap up an app that runs in a WebView that has additional native extentions, which is the definition of a hybrid app. Cordova is the open source platform that the original PhoneGap became.
Ionic Framework is based on Cordova, comes with a set of standard controls that mimic native controls, and Ionic comes with Angular. Using Ionic with Angular can help you organize your app and give it a solid look. Ionic also includes bindings to the Ionic services. Seefor more information.
PhoneGap at this point is based on Cordova, but is more of a distribution of Cordova with few custom packages and tweaks. Adobe also provides a build service.