What are "post-deadline paper submissions"?
You can think of post-deadline submissions as reserving seats on overbooked flights: if someone doesn't show up, you get the place. But in case of conferences, not that automatically.
Some twenty years ago, when conference submissions were handled through emails, post-deadline submissions were not that uncommon, at least in my field. You would have sent an email apologizing for not having been able to respect the deadline, and hoped for the best. If the technical committee found your work valuable and the organizers could find a free slot, either oral or poster, your paper would have been accepted and your submission would have been added to the book of abstracts as a spare sheet with the headline "post-deadline submission". I recall conferences with around 5-6 post-deadline submissions.
With the advent of submissions managed through websites, it seems to me that post-deadline submissions have been progressively less accepted.
Do post-deadline papers get vetted differently, or do they basically receive an extended deadline?
How post-deadline submissions are handled really depends on the conference organizers, and how much post deadline the submission is. In some cases, they could be reviewed directly by the chairs of the technical committee rather than by the designated reviewers.
I've sat on journal committees and reviewed proposals. We know that for many people, their institution won't pay unless they are presenting. So we want to make as many slots as possible. If there is a possible to squeeze in a few more talks or posters after the deadline (because we found another venue, or didn't get enough in the first place), we'd open it up for post deadline submissions. The bar might be a little higher, but only a little. (I can imagine that for some conferences, the bar might be lower.) It's a slight pain, because things have to be reviewed more quickly, so we would rather not do it.
Other conferences are much more selective, and this would not apply to them.
That might not be how it works for every conference. If they announce post-deadline submissions before the deadline, then I have no idea.
Post-deadline submissions, at least within optical communication, are also intended for "new and significant material in rapidly advancing areas".
From the OFC 2020 website:
Postdeadline submissions are not an opportunity to submit a paper after the published deadline, but are intended to provide those with late-breaking work an opportunity to submit that work for consideration. Postdeadline submissions should describe new and significant material in rapidly advancing areas. A limited number of postdeadline submissions will be selected for presentation, and only those papers judged to be truly excellent and compelling in their timeliness will be accepted.
https://www.ofcconference.org/en-us/home/submit-papers/submit-papers/#Postdeadline (Accessed 2020, March 5)