Azure App Service, Mobile Apps or Api Apps; what is the difference?

Azure Mobile Apps are the next version of Azure Mobile Services. Azure Mobile Services has been deprecated, and you can't provision it on new subscriptions. Mobile Apps has a lot more features over Mobile Services. To learn more, see I use Mobile Services, how does App Service help?.

Mobile Apps, Web Apps, and API Apps are all essentially the same thing, they just have some extra features for building particular solutions. You publish each of them to an App Service Plan, which is the actual underlying VM that hosts your service.

Once you've provisioned one of these app types, you can publish a Web API to it, regardless of what app type it is. For instance, you can publish your API to a Web App or Mobile App. Once you've picked a particular app type, you aren't locked in, you will just see a slightly different UI in the Azure Portal.

Mobile Apps also have a Mobile Server SDK for Node.js or .NET. The .NET server SDK is an extension of ASP.NET Web API. It doesn't yet support ASP.NET 5, mainly because there is a dependency on the OData library, which doesn't yet support ASP.NET 5. However, Mobile Apps is under active development and will support ASP.NET 5. Unfortunately, we don't have a timeline to share, mainly because not all the dependencies are complete.

For Mobile Apps in particular, you get the features of client SDKs that support authentication, offline sync, and push notifications. The easiest way to learn about the offering is to follow the quickstart guide: Create a Windows app on App Service.

You can learn all about the SDK and try them out, even without an Azure Account. Here's documentation about the .NET server SDK: Work with the .NET backend server SDK for Azure Mobile Apps.

API apps have a few extra features like creating a metadata endpoint for you automatically, which you can then use to generate client library using Visual Studio.

Currently, only Web Apps and Mobile Apps have a demo experience available at Try App Service, but you can see the API experience if you use a Microsoft Account to sign in, and then manage the app in the Azure Portal. You will see all of the API app and Mobile App options in the portal.

Note that Web and Worker roles are part of Cloud Services, and are a totally separate service. To learn about the difference between these, see Azure App Service, Virtual Machines, Service Fabric, and Cloud Services comparison.