what is the difference between data adapter and data reader?

Data Reader is an object used in connected Environment. Data Adapter is an object used in Disconnected environment using Dataset.

Please see DataReader, DataAdapter & DataSet - When to use? :

ADO.NET provides two central Data Access Components. The excellent thing is that, they are common across all Databases, be it SQL Server or other competitive databases. Its only the namespace to be used, that differs, while using a Database other than SQL Server.

A DataReader is an object returned from the ExecuteReader method of a DbCommand object. It is a forward-only cursor over the rows in the each result set. Using a DataReader, you can access each column of the result set, read all rows of the set, and advance to the next result set if there are more than one.

A DataAdapter is an object that contains four DbCommand objects: one each for SELECT, INSERT, DELETE and UPDATE commands. It mediates between these commands and a DataSet though the Fill and Update methods.

DataReader is a faster way to retrieve the records from the DB. DataReader reads the column. DataReader demands live connection but DataAdapter needs disconnected approach.