The issue presented here is most likely result of a small misconception that is all the easier that the modern animals we know as 'pigs' has been selectively bred for millennia with the very intensified refinement occurring in the last two centuries as permitted by good understanding of genetics and development of modern breeding methods, resulting in a distinctly different animal. From the biological standpoint though, 'boar' and 'pig' are exactly the same species, i.e. Sus scrofa. The aforementioned misconception might has been propagated by the usage of the expression Sus scrofa domestica to denote a domesticated pig, but this is incorrect term, possibly created by the unwarranted omission of the abbreviation 'f.' before the last part of the name, as the full scientific name is Sus scrofa f(orma) domestica, indicating that this is just a difference of some physical properties caused by selective breeding, but pigs and boars are essentially the same animals. Not unlike virtually all breeds of dogs, despite colossal differences, are basically all examples of a single species, i.e. Canis familiaris.

Now, the 'boars' that can be encountered in Americas and Australia are basically domesticated pigs, usually of the subspecies Sus scrofa scrofa or the most common European boar that escaped and then they went feral. It is worth mentioning though that the pigs that have been brought to Americas since 16th and to Australia since 18th century (especially the former) were somewhat different from what we know today. They were still covered with abundant, dark, three-layer coat with prominent mane running the entire length of the back and had body proportions more typical to a wild boar than modern domesticated pig (noticeably lowered pelvis, massive shoulders and long, triangular snout). This can be seen on the contemporary depiction of pigs that are quite numerous, given the ubiquity of the animal both in figurative paintings (especially by Dutch painters of 16th century) and allegorical works. They were far cry from e.g. Large White (Yorkshire) breed similar to the stereotypical depiction of a modern pig.

In other words, the boars one can encounter in America and Australia were the same animals that were introduced there and herded as a livestock by colonists. They were docile to some extent, but still required some skill to herd (but again, horses and cowns can also be very dangerous if handled or even approached improperly). Due to eurytopical character of these animals (an ability to thrive in relatively wide range of natural circumstances), they were able to adjust to the new biotop and multiply, quite quickly returning to their apparition of a wild boar they did not move too far from in the process of domestication.