The name PhoneGap and Apache Cordova are often used interchangeable. PhoneGap was originally a product of Adobe, but was later donated to the open-source community and rebranded as Apache Cordova. The concept is quite simple, imagine a traditionally web application squeezed into a mobile application. The mobile app itself is basically a browser rendering HTML and CSS in the form of an iOS or Android app. This allows developers to create a cross platform mobile app using their existing web development skill set.
React Native is the newcomer to the world of mobile cross platform development and we can thank the folks at Facebook for sharing their framework with the open-source community. It follows most of the same principles as Cordova, but instead of HTML it uses a custom UI layer based on their React technology. This subtly difference resolves the performance and responsiveness that commonly plague Cordova applications. However, React Native currently only supports iOS and Android, but they are slowly expand their supported platforms.
Regardless of which technology is used, the outcome is the same. A single application that can be deployed to multiple mobile platforms. Cross platform mobile apps