You can copy data from one table to another no matter both the tables are in same database or different databases.
Let say you have two tables named table1 and table2 in database named db1.
Following query copies all the data from table1 to table2 in same database
INSERT INTO `db1`.`table2` SELECT * FROM `db1`.`table1`
Following query copies all the data from table1 of db1 to table1 of db2
INSERT INTO `db2`.`table1` SELECT * FROM `db1`.`table1`
Note: For above queries both the tables must have same schema, means the number of columns , their names and data types.