What constitutes a Via-in-Pad?
I would think about it this way, why would you care if a via was "via in pad"?  Because you want to treat it a special way, and perhaps because that treatment will cost you more at fabrication. So why treat a via that's in a pad any different?  For me with a through hole via in pad I'm worried about solder wicking through the barrel of the via and possibly to the back of the board.  Either way it's the ultimate mechanical, electrical, and possibly thermal connectivity of my joint that I'm worried about.

To fix that we usually fill the vias with either conductive or non-conductive fill and then plate them flat (I've been using non-conductive lately because it saves a step).  

Now to your question, when would I treat a via specially and call it via in pad in these cases?  I would say it's anytime I think solder might flow into that hole.   So perhaps even your first example if there is not enough clearance for solder mask between the hole and the pad so that no solder will flow in the worst case.  Even your second case might warrant it if there's not enough room for solder mask, that's something I would expect to get flagged at DFM.

On an interesting side note at our fabs once you do one via in pad it costs no more for us to do everything via in pad.  So if you find yourself having to make that decision for one case maybe you can do it everywhere.