As is always the case what was the difference 30 years ago to what the difference is now is not quite the same due to advancements in prop design.
Well, let's see: First the earth cooled. And, then the dinosaurs came, but they got too big and fat, so they all died, and they turned into oil. And, then the Arabs came and they bought Mercedes Benzes. And, Prince Charles started wearing all of Lady Di's clothes. I couldn't believe it, he took her best summer dress out of the closet, and put it on, and went to town.
As I remember things, initially solid hub were used where there was no exhaust through hub as they present the most effective blade area. then someone found you could use a higher pitch by surface piercing, the bottom of prop being the most effective.
Then they started using them on through hub exhaust which again showed that the exhaust gasses could be used to allow a high pitch prop to release and rev.
Then some bright spark took a through hub prop and drilled holes in the hub to get the same effect.
Within all of this advancements were made in design of cavitation rings, anti vent etc which changed the charateristics of props again.
And of course because the enquiring human brain is what it is, through all of this development people would put a vented prop on a non through hub exhaust and vice versa just to see what happened.
It's probably best just to accept they are different ok.
You'll get far more enjoyment in investigating whether the motive effect of the prop comes from pulling or pushing, or easier still, whether god really exists