The group in Machir are identified by the bible as having been well fortified with high walls and gates (Deuteronomy 3:4-5, Joshua 13:30, 1 Chronicles 2:23), and in the time of Solomon are said to have formed a part of Ben-geber's commissariat district (1 Kings 4:13). This group are clearly identified by the bible as having been the main towns of the Argob, a rocky region in the otherwise gentle plain of Bashan, and having been originally ruled over by king Og, before Israelite dominion.
The name Havoth-Jair can mean hamlets of Jair, and the bible portrays these as having been founded by a person named Jair who conquered the previous towns and villages in these locations; in the case of the villages with Machir ancestry it is a Jair named as a son of Manassah, while those with Gilead ancestry are identified as being founded by a Jair who is a Gileadite. According to critical scholarship this is likely to be folk etymology, particularly as in the eyes of archaeologists, the Israelite invasion of Canaan (and hence Jair being the particular conqueror for these locations) is non-historic, and the Israelites were most likely just a group of Canaanites. Translating Jair, the name Havoth-Jair is seen to mean hamlets of the enlightened one, and could in fact be a reference to Og, or another ruler.
It is thought possible that the three groups of towns in fact refer to the same set of places, but that the different reports of ancestry and locations reflect the geo-political circumstances of the towns and villages, in the time periods that each particular part of the bible were written.