At my all boys English grammar school in the 60s both methods were in use but I never really understood the rhyme or reason. If you misbehaved in class the master would often call you out to the front of the class and deliver a good whacking on your behind with a plimsoll in front of the class. Other times he would tell you to report to him after class and give you the slipper in private.
I suppose one advantage from the teacher’s point of view of giving a boy a vigorous spanking in front of the class was the deterrent value to all the other boys. On the other hand telling the boy to report after class to have his bottom slippered meant less disruption to the flow of the lesson.