Not quite right.

The expression "CAST('321a' AS INTEGER)" will do as you suggest and ignore the trailing 'a' character, yielding an integer 123 result. But that only happens for an explicit CAST. Automatic type conversions must be reversible. That means that '321a' is inserted as a string in an INTEGER column, but '321' (without the trailing 'a') will be converted into an integer 123.

PostgreSQL, MySQL, and SQL Server do exactly the same thing for the '321' case. For the '321a' case, the other three throw an error whereas SQLite just cancels the type conversion and inserts the original string.