Not really, no. It's really nit-picking, but a "via" is a (usually small) plated-through hole that is used solely for connecting traces on different layers of the board. I'm pretty sure the term isn't normally used for the plated-thru holes with pads that are used for thru-hole parts, even though the construction of the two is almost the same. The main differences are that the holes for PTH parts are usually larger, and the pads around them are larger, for better soldering. Vias don't need much of a pad around the hole because you're not putting solder in the hole, and vias are usually covered with soldermask.
Yes, really, yes. It isn't nitpicking when you're simply wrong. Via's are vertical interconnects between layers, they can be 'blind' vias which do not connect to either top or bottom layers or regular ones.
"Plated-through holes are no longer required with SMT boards for making the component connections, but are still used for making interconnections between the layers and in this role are more usually called vias.[2]"
Even your own link says nothing about PTH, and just discusses vias for use in SMT.
