Data Exchange between different MySQL Databases

To exchange data between different MySQL databases use the INSERT…SELECT syntax.

If both tables are identical:

INSERT INTO database2.table1
SELECT *
FROM database1.table1
WHERE 1;

To insert the value of selected columns use:

INSERT INTO database2.table1 (column1)
SELECT column1
FROM database1.table1
LIMIT 1;

This only works, if both databases are hosted on the same MySQL server! There is absolutely no way to exchange data between different/remote MySQL servers using standard (My)SQL syntax!

If you intend to access data from different/remote MySQL server, use the FEDERATED storage engine (cf. the MySQL website), which allows you to execute local queries on the remote database.