I was confused enough by the explanation that I had to try this myself. Two statements in the explanation are contradictory (emphasis mine):
... COUNT_BIG(all column_2) will count all rows from the table (including duplicate & null rows). COUNT_BIG(DISTINCT column_2) will evaluate distinct non-null values.
ALL is the default and hence COUNT_BIG(column 2) is same as COUNT_BIG(ALL column_2). This evaluates expression for each row in a group and returns the number of nonnull values. ...
II and III are correct, by the way.
Ed Leighton-Dick | Consultant | Microsoft Data Platform MVP | MCSE | PASS Regional Mentor