DataTable is a Table for storing in-memory data.
DataSet is a collection of DataTables.
Please refer to the following link to know the differences between DataTable and DataSet,
dataset act as container for data table...
Difference between data table and dataset is , Datatable is collection of rows and columns and Dataset is collection of tables both are used in disconnected architecture .
Data table means collection of rows and columnsData Set means collection of Data tables
A database is a collection of information organized to provide efficient retrieval,it is a mechanism for storing, managing,updating and retrieving information.