The best guess for a pad stack is just that a stack of pads. One on the top and one on the bottom layer. Pads have holes and usually are plated through.
VIA's don't have to have holes. There are blind and burried VIA's. On a two sided board, they connect the top and bottom layers.
KISS's definition might also include that "a padstack ...for four or more layers the pads on different layers could be different sizes for the same hole".
A padstack defines a pad which is usually a contact point for the lead of a component, or in other words, its the pad that the component is soldered to. A via is not for component leads, it is only a transition between layers. Different rules are applied to each.
I think he was saying that a via may not have a hole that goes all the way through the board. The holes in blind and buried vias don't go all of the way through. Also, a via hole can be filled with copper plate by the PCB fabricator such that there is no longer a hole.
As for pad stacks. I frequently change a pad to have different pad sizes on different layers. For instance, a through hole connector will have a larger pad on the 'solder' side to facilitate hand soldering, but have a small pad on the component side allowing for more top side traces to go between the pads.
I think he was saying that a via may not have a hole that goes all the way through the board. The holes in blind and buried vias don't go all of the way through. Also, a via hole can be filled with copper plate by the PCB fabricator such that there is no longer a hole.
As for pad stacks. I frequently change a pad to have different pad sizes on different layers. For instance, a through hole connector will have a larger pad on the 'solder' side to facilitate hand soldering, but have a small pad on the component side allowing for more top side traces to go between the pads.