"Today I Learned" or little things I learned day by day.
INSERT INTO `database`.`table_new`(`colA`,`colB`,`colC`)
SELECT `colA`,`colB`,`colC`
FROM `database`.`table_old`
This works even between tables with different column structures. Only related columns must be same.
Another example with more tables
INSERT INTO `table_new`(`colA`,`colB`,`colC`,`colD`)
SELECT `colA`,`colB`,`colC`,`colD` FROM `table_old_1`
UNION ALL
SELECT `colA`,`colB`,`colC`,`colD` FROM `table_old_2`
UNION ALL
SELECT `colA`,`colB`,`colC`,`colD` FROM `table_old_3`;