Is there a distance minimum? Any other requirements?
As an example of a trail I think might be on the board I am thinking about the High Sierra Trail. It is only 50 miles. Work was started on it in 1928. It was the first trail in the Sierras to be built solely for recreational use. But I’m biased. It holds a dear place in my heart being the only trail I’ve done at least a significant part of almost every decade of my life. There is a wikipedia page at High Sierra Trail - Wikipedia
Good question!
I don’t think there’s actually a distance minimum (though I may be wrong). From what I understand, a thru-hike is an act of hiking an established route from start to end. I think it was popularised by hikers who attempted the really long trails like the AT, so there’s probably some attachment to really long-distance because of that.
For me, the High Sierra Trail would count 
I just watched this video of a couple doing it and it looks so beautiful! What a treat it must be to be able to hike that regularly.
In my experience I start to look for hikes starting at 50km. If I am only hiking for a weekend sth shorter (2 full days/50 km/1500m elevation) and for the big tours 200+km. One important date for me is elevation. I plan my days mostly after elevation and accommodation/camping and less for distance.
I always thought of thru hikes as a trail that doesn’t have the same start and finish point. Didn’t factor in distance to the mix. There have been some day hikes I would consider thru hikes cause I would take one trail up the mountain and another trail down to a different park exit