I would assume pigtails are braided, based on kids books like Pippi Longstocking. But I would use the term for more modern, unbraided hair also.
ETA: Wikipedia agrees. Apparently the twist of the braid is where the term comes from.
The term pigtail appears in English in the American colonies in the 1600s to describe a twist of chewing tobacco. One of the steps in processing the tobacco was to twist a handful of leaves together to form a compact bunch that would then be cured (dried, either with or without smoking). The term "pigtail" was applied to the bunch based on its resemblance to a twisted pig's tail.
From the later 1600s through the 1800s, the term came to be applied to any braided (plaited, in British parlance) hairstyle. The British army also adopted a single pigtail or "queue" as its standard dress for long hair.
Most dictionaries still define "pigtail" as a single tight braid. However, many American English speakers use the term to describe two symmetrical bunches of hair on either side of the head, braided or not.