The two approaches to building applications with Expo tools are called the "managed" and "bare" workflows.
In the bare workflow you can use any Expo library and service, and you are responsible for the native iOS and Android projects.
If you've used React Native without any Expo tools then you have used the "bare workflow", but the name probably doesn't sound familiar. It's easier to talk about something when it has a name, so we call this "bare" – somewhat in jest, and because of the existing term "bare metal". If you have direct access to the native code it's a bare project. The "Already used React Native?" page might be useful for you to quickly understand where Expo fits in.
Developers build managed workflow apps using expo-cli on their computer and a development client on their mobile devices (either the Expo Go app for more simple projects or a development build when your project grows). Managed workflows apps typically use one or more Expo services, such as push notifications, build, and updates.
While you can do a lot with the managed workflow, you can't do everything with it, so what are your options when you encounter a limitation?
If you get to the point where you need to have full control over the native code in your app, you can generate the native projects and continue development using the bare workflow. You can do this by running expo prebuild.
In the bare workflow, the developer has complete control, along with the complexity that comes with that. You can use all packages from the Expo SDK, development builds, and all Expo and EAS Services. Configuration with app.json/app.config.js is mostly not supported in this context; instead, you will need to configure each native project directly.
Expo never locks you in, you can generate the native iOS and Android projects from your managed project at any time you like. You can use one library or service or many, in managed or bare projects.
If you are new to mobile development or new to development, in general, we recommend that you use the managed workflow. There is a huge amount of complexity that comes along with the native development toolchain and the managed workflow allows you to deal with that complexity only when necessary.
If you are more experienced it also doesn't hurt to start every new project with the managed workflow and only generate the native projects when needed.
In summary, use the bare workflow when you need it due to limitations, otherwise use the managed workflow, and you most likely want to start with the managed workflow.
Text can only go so far - if you want a more complete picture of building an app end-to-end with the managed workflow, you should continue to the Walkthrough page. There are a bunch of videos and it's easy to skim through, and you should leave it with a better sense of what building a managed app looks like. Go watch them now.