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,http://onlydifferencefaqs.blogspot.in/2012/08/difference-between-datatable-and-dataset.html
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.