The column names do not matter at all, as long as data types match (or can be cast in the assignment).
If the data types of the columns don’t match, try casting the values accordingly. Just try with small dummy tables. Be sure to list the target columns explicitly to avoid confusion. Like this:
INSERT INTO TableB (b1, b2, b3)
SELECT a1, a2, a3
FROM TableA
WHERE <some condition>;
More details in the SQLite manual here.