***** NOT A TEACHER *****
(1) As I understand it:
To liken two things (to say that X = Y; Y = X).
Mother (angry): You are just like your brother.
Tom: No, I'm not. Stop comparing me to him.
To show the similarities and the differences between two things.
How would you compare life in your country today with life in
your country ten years ago?
Compared with Westerners, Asians eat more vegetables.
(3) Of course, many native speakers do not follow this rule, for
many do not know this rule. So do not be surprised if you see
these terms used interchangeably.