What is the difference between using remote as and local as in bgp?

Remote-As-

This keyword with bgp neighbor statement is used to define as no. of neighbor.

Local As-

This keyword is used in case of AS migration, when one service provider purchase another service provider.Its not possible to change all customer configuration at once, so at provider end we use local As keyword to form neighborship.

neighbor AS2 remote-as 200                  nbr AS1 remote-as 100                                    nbr AS2 remote-as 200

                                                           nbr Cust remote-as 300

So Cust in AS 300 has formed neighborship with AS 200(Airtel).Assume Tata purchases Airtel, so tata want to use its own As no. in airtel's network, but the problem is customers still have As 200 configured in neighbor statement.

New Scenario will look like:-

Now on all airtel routers as we are running As 100, we need to run local as feature on all routers connected to customers so that customers can still form neighborship with AS200(OLD AIRTEL).

neighbor AS2 remote-as 200                 nbr AS1 remote-as 100                                nbr AS2 remote-as 200

                                                          nbr Cust remote-as 300

                                                          nbr Cust local-as 200

So, now there is no need to change any configuration on customer end.