This code selects data out of a table and displays it in the query tool (usually SSMS)

SELECT Column1, Column2, Column3 FROM MySourceTable;

This code inserts that data into a table:

INSERT INTO MyTargetTable (Column1, Column2, Column3)
SELECT Column1, Column2, Column3 FROM MySourceTable;

This code selects data out of a table:

SELECT Column1, Column2, Column3 FROM MySourceTable;

This code creates a new table called MyNewTable and puts that data into it

SELECT Column1, Column2, Column3 
INTO MyNewTable
FROM MySourceTable;

To move data you first insert it into the target, then delete whatever you inserted from the source table. This is not a normal SQL operation but it may be enlightening

What did you insert? Normally in databases you need to have one or more columns that you can use to uniquely identify rows so we will assume that and make use of it.

This statement selects some rows

SELECT Key1, Key2, Column3, Column4 FROM MyTable;

First we insert these into our target table:

INSERT INTO TargetTable (Key1, Key2, Column3, Column4)
SELECT Key1, Key2, Column3, Column4 FROM MyTable;

Now assuming records in both tables are unique on Key1,Key2, we can use that to find and delete data out of the source table

DELETE MyTable
WHERE EXISTS (
    SELECT * FROM TargetTable 
    WHERE TargetTable.Key1 = SourceTable.Key1
    AND TargetTable.Key2 = SourceTable.Key2
);

This will only work correctly if Key1, Key2 are unique in both tables

Lastly, we don't want the job half done. If we wrap this up in a transaction then either all data will be moved, or nothing will happen. This ensures we don't insert the data in then find ourselves unable to delete the data out of the source.

BEGIN TRAN;

INSERT INTO TargetTable (Key1, Key2, Column3, Column4)
SELECT Key1, Key2, Column3, Column4 FROM MyTable;


DELETE MyTable
WHERE EXISTS (
    SELECT * FROM TargetTable 
    WHERE TargetTable.Key1 = SourceTable.Key1
    AND TargetTable.Key2 = SourceTable.Key2
);

COMMIT TRAN;