To me - a 52 year old American - native to this country...
To me - if it's braided and hangs freely, then it's a pigtail.
If it is NOT braided and hangs freely, then it's a ponytail.
So, to me, the first picture is of a girl with two ponytails.
The other two pictures are of pigtails - the first one has two pigtails, the other one only has a single pigtail.
I know - the definition of a ponytail is that it's pulled back and hangs loose from the back of the head. But the 'hangs loose' is the important aspect of a ponytail - hangs loose like a pony's tails does.
Pig's tails, however, have very little in the way of fur or anything - until the end, then they have a little tuft of hair - which is similar to the appearance of a braided hair - tightly woven, until the end, then a little tuft of hair after the rubber band holding the braid in place.
I think plait and braid are essentially the same thing. However, a pigtail is a braid that hangs freely. Whereas a braid/plait that is then tied into a top-knot would still be a braid, but would no longer be a pigtail.
Hope this helps...
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