The software was previously called just “PhoneGap”, then “Apache Callback”. As open-source software, Apache Cordova allows wrappers around it, such as Appery.io or Intel XDK.
PhoneGap was Adobe’s commercial version of Cordova along with its associated ecosystem. Many other tools and frameworks are also built on top of Cordova, including Ionic, Monaca, VoltBuilder, TACO, Onsen UI, Visual Studio, GapDebug, App Builder, Cocoon, Framework7, Quasar Framework, Evothings Studio, NSB/AppStudio, Mobiscroll, the Intel XDK, and the Telerik Platform. These tools use Cordova, and not PhoneGap for their core tools.
Contributors to the Apache Cordova project include Adobe, BlackBerry, Google, IBM, Intel, Microsoft, Mozilla, and others.