If both the tables are exactly the same schema, use the following code:
INSERT INTO newTable
SELECT * FROM oldTable
If the schema is not same, you will need to mention the column names (the column list for newTable is optional if you are defining a value for all columns and selecting columns in the similar order as newTable's schema):
INSERT INTO newTable (col1, col2, col3)
SELECT column1, column2, column3
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