Android Database:

Android's Java interface to its relational database, SQLite.

It supports an SQL implementation rich enough for anything you're likely to need in a mobile application, including a cursor facility.

ContentProvider:

An interface used between applications.

The server application that hosts the data manages it through basic create, read, update, and delete (CRUD) operations.

The client application uses a similar API, but the Android framework transmits the client's requests to the server.