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.