react-native start is same as npm start and like you said it's to start the 
react packager/server.

I have found myself in situations where I had to stop and start the server 
explicitly using npm start.

To start up a project, you use the react-native run-ios and it starts up both 
the simulator and the server but in cases where the app has been installed and 
you want to restart the server, you can stop it explicitly in the terminal and
use react-native start or npm start to start it up again.