Data table means collection of rows and columns

Data Set means collection of  Data tables

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 .

A database is  a collection of information organized to provide efficient retrieval,it is a 

mechanism for storing, managing,updating and retrieving information.