I can think of one difference, although it's hard to relate to the corporate environment.
But within a school for instance, the I would say corporal punishment (now generally not permitted) would involve actually physically striking the body of the 'offender' - from slapping the wrist through to an actual caning or slippering.
Physical punishment could just be being made to do 100 press-ups, or running round the playing field 5 times, or standing on your head for 30 minutes - do you see what I mean.
However, like I say, while I can see a difference, I can't really relate either type of punishment to a corporate situation!