Example A
SELECT column_name(s)
FROM table1
LEFT JOIN table2
ON table1.key = table2.key
WHERE table2.key IS NULL;
Example B
SELECT column_name(s)
FROM table1
LEFT JOIN table2
ON table1.key = table2.key AND table2.key IS NULL;
Would the two SQL queries above be logically equivalent or what is the point of filtering within the ON?
Example1 - WHERE clause condition filters the final result so your example1 returns data from table1 for which matching data is not present in table2 as left join is based on key and after that where condition filters all the records that have no matching key in the table2 - you will find less than or equal to total table1 record in the result
Example2 - Condition in the ON is used to join two tables so your example2 will give you all the data from table1 and only matching data from table2. But as you have used conflicting condition in the ON clause (ON table1.key = table2.key AND table2.key IS NULL), your example2 will return all data for table1 and no data for table2(null in all columns for table2) - final result will have number of records equal to number of records in table1.
Example B will JOIN nothing because ON clause will be always FALSE.
So technically your Example B is equal to:
SELECT my_column
FROM table1
When Example A will return all records from table A which have no matching records in table B.