Disambiguation from Wikipedia (long word also courtesy of Wikipedia)
"A pigtail is another name for hair styled into a large braid that extends down or out from the head. In analogy to the ponytail hairstyle and the long, free-flowing tail of a horse, a pigtail is named for the visual resemblance of a thick, irregularly-tensioned hair braid to the kinked tail of a pig. A person's hairstyle may consist of one or more individual pigtails.
In some regional usages of English, pigtails are considered synonymous with a symmetric pair of hair bunches, regardless of whether each "bunch" is braided or left loose. This usage is not evident in American literature where one frequently finds references to "two pigtails" denoting two braids."
Personally I would say:
ponytail = one, left loose
plait = one, plaited (AKA 'braid' in US English)
bunches = two, left loose
pigtails = two, plaited
My 'rules' for wearing these: plait or ponytail is fine for anyone.
Bunches or pigtails coming out of your head above the ear: recommended only for children, fancy dress, or people whose style is a bit 'kooky'. If you wear purple stripey knee socks then go ahead (but of course if that is your style then you don't need my permission). If you're wearing 'normal' clothes then you might expect a few odd looks, but people are genrally more polite in real life than on a thread that starts with 'am I being unreasonable'.