Not to start directly with the differences, lets look closely into what exactly are these two Mobile applications.

What are they?

React Native Applications are primarily built on JavaScript which makes it possible for a developer to share the code across various diverse platforms where it renders native components. It is built in the language that is required to target a platform, as for react native iOS it is Objective-C or Swift, and Java for Android. The code written to develop an app is not shared and the app has access to all features of a platform for which the app is built without any interruption.

Hybrid Apps are built on HTML, CSS and JavaScript, they are at the core websites which the exterior of a native application. Thus, we can say they are something in between Websites and Native Mobile Applications. At core being a website, what makes it like a native app is their feel, there controls and navigating elements are a lot like native mobile applications. They are websites built on HTML5 and JavaScript wrapped in a native container. And the basic difference between a Hybrid App and Native Mobile App is the native app loads the important data and content on the first installation, while Hybrid app loads the data continuously as the user navigates across the application.

What are the differences?

Write once, run anywhere

This is one the latest trends which allows developers to create mobile applications for various platforms by using a single codes base.

React Native
One of the major differences between the two applications is React Native is not built to serve WORA (Write Once, Run Anywhere) rather it is built to give React developer opportunity to exploit various components of diverse platforms, in short it is built to render native components and native behaviour of a platform onto an application.

Hybrid Applications
As for Hybrid Mobile Applications, they are built on the objectivity to sweat out WORA effect, they are built for using a single code base regardless of a platform and use Cordova and PhoneGap toolsets to utilize native features such as GPS, Camera etc.

The Language Stack

Various set of languages used together for developing and application or a website is known as Language stack, like JavaScript, HTML, CSS, C+, C# etc.

React Native
React Native is built on using JavaScript and its native frameworks, as it is based on JavaScript framework React. It resembles somewhat like HTML and was initially called JSX. In it the display logic is blended with business logic.

Read More About- Angular vs. React: Which Is Better for Web Development ?

Hybrid Applications
Hybrid Mobile Applications are built on Angular which is a JavaScript framework and uses HTML templates for its views. That makes it somewhat like React Native right, but no the basic difference is in the Model-View-Controller Architecture in which views and logic are separated. Other Hybrid Mobile App development languages are

Testing During Development

Testing an essential part of Mobile Application development, which allows you to test the functionality, response and UI and UX of a mobile application.

React Native
React Native has amazing feature that helps developers see results of their coding modifications in real-time which eliminates the need of recompiling, rebuilding and other time and money consuming phases of development. It is an amazing way to test your app while you are still coding making it possible for you to test instantly the app in an emulator or a device.

Hybrid Applications
You can see your app preview in the browser and a mobile device almost instantly, it refreshes the changes and updates the application as soon as you make the changes.

Plug-in and Community

Plug-ins and Community support are two ways that help you differentiate between a good and a so-so platform. Plug-ins on one hand gives your development a great functionality and extensibility while a large community support ensures a great developer following and working on different development aspects of platform and the help you will be able to exploit in case you got stuck.

React Native
There are numerous of Plug-ins available for React native on NPM, to add more there is even a plugin to add Cordova and PhoneGap Plug-in. react native is thus a very efficient platform to build an application, it allows you to gain access of various mature plugins from various communities instantly.

Hybrid Applications
You can sell and offer Ionic plug-ins at a Marketplace to exploit Native features during Hybrid App Development.

User Experience

User Experience play an important role in a success of an app and attracting more and more loyal user base.

React Native
Due to its native qualities, it is able to create a better user experience, it is much clearer and Native feel of an application makes it possible to add many motions and gestures, in short catering a great user experience to the users.

Hybrid Applications
The basic thing that we forget during Hybrid Mobile App Development is that they are actually more like web pages, collecting data from websites thus affecting its performance largely. Its working on many Flagship Smartphones will just be fine as it wont be able to access a lot of device APIs and be confined to basic features such as GPS and device Webview.