As you noticed React Native is not based on Cordova. It is not a website which looks like an app shoveled into a WebView.
React Native uses a JavaScript runtime, but the UI is not HTML and it doesn’t use a WebView. You use JSX and React Native specific components to define the UI.
It provides a native-level performance and look and feel but some UI parts have to be configured separately for iOS and Android. For example Toolbars are completely different, but TextInput can be the same for both Operating Systems.