PhoneGap is a library that exposes native mobile phone functionalities as JavaScript API. When Adobe purchased PhoneGap, its open source core was donated to the Apache Software Foundation under the name Cordova. In the beginning, there was almost no difference between Cordova and PhoneGap. Although, over the years of development, Adobe started adding a proprietary set of the services to PhoneGap. Today, it is safe to say PhoneGap is Cordova plus extra Adobe services.
Ionic uses Cordova, not PhoneGap for its core tools. Beside native mobile phone functionalities, Ionic gives structure and code scalability to JavaScript applications by using AngularJS (Angular, React and Vue for IOnic 4). It also provides a set of Angular directives and components to speed up application development.