npm start is the short form for npm run start
You can check about it here Difference between npm start and npm run start
react-scripts start
react-scripts is a set of scripts to support the creation, development and testing of react applications. It is used by create-react-app.
create-react-app is the officially supported way to create single-page React applications. create react app uses webpack to parse and bundle the application.webpack parses the application and creates a dependency graph from its entry point specified in the webpack config file. while parsing, webpack uses babel to transpile the application to JavaScript, which has better support across browsers.Webpack uses the generated dependency graph to create a single JavaScript file consisting of the application source code and modules used by the app, injects the file via script tag into public/index.html, and starts a development server on http://localhost:3000. Navigating to this URL in the browser will show a live, interactive instance of your application. Any changes saved to the source code will reflect in the running app instance automatically.You can read more about this topic more on here