I was reading this wikipedia article about an elite military force in Egypt which began as an ethnic tribe from the deserts of the eastern Sudan. This tribe was called Medjay. It was mentioned that some of the Medjay had Egyptian names and were depicted as such in wall paintings. Egyptologists say that this was due to the influx of ethnic Egyptians into this group.
While researching on this, I encountered something curious in page 164 of Herodotus' Histories book II.
 The Egyptians are divided into seven distinct classes - these are, the priests, the warriors, the cowherds, the swineherds, the tradesmen, the interpreters, and the boatmen. Their titles indicate their occupations. The warriors consist of Hermotybians and Calascirians, who come from different cantons, the whole of Egypt being parcelled out into districts bearing this name.
He also expanded on the warrior caste in page 168
 The warrior class in Egypt had certain special privileges in which none of the rest of the Egyptians participated, except the priests. In the first place each man had twelve arurae of land assigned him free from tax. (The arura is a square of a hundred Egyptian cubits, the Egyptian cubit being of the same length as the Samian.) All the warriors enjoyed this privilege together, but there were other advantages which came to each in rotation, the same man never obtaining them twice. A thousand Calascirians, and the same number of Hermotybians, formed in alternate years the bodyguard of the king; and during their year of service these persons, besides their arurae, received a daily portion of meat and drink, consisting of five pounds of baked bread, two pounds of beef, and four cups of wine.
He described them as Hermotybians and Calascirians. What are the meanings of these names in the greek language?
Are these groups the same as the Medjay?
As for the Medjay, I want to know if it has become possible for archeologists to locate their modern descendants.
The Hermotybians and Calascirians mentioned by Heordotus appear to be simply two parts of the Egyptian army, each recruited from particular parts of the country. Indeed, Hordotus himself makes this explicit:
"Their warriors are called Calasiries or Hermotybies and they are of the following districts, for all Egypt is divided into districts.
The following are the districts of the Hermotybies:Busiris, Sais, Chemmis, Papremis, the island called Prosopitis, and the half of Natho. From these districts are the Hermotybies, being in number, when they are most numerous, a hundred and sixty thousand. None of these learn any mechanical art, but apply themselves wholly to military affairs.
These next are the districts of the Calasiries: Thebes, Bubastis, Aphthis, Tanis, Mendes, Sebennytus, Athribis, Pharbaethus, Thmuis, Onuphis, Anysis, and Myecphoris; this district is situated in an island opposite the city of Bubastis. These are the districts of the Calasiries, being in number, when they are most numerous, two hundred and fifty thousand men… "
- Herodotus Histories Book II
This division of the army into two parts was not something introduced by the Greeks, but is also attested in much earlier records.
For example, the Great Edict of Horemheb states that:
The two divisions of troops which are in the field, one in the southern region, the other in the northern region, stole hides in the whole land, not passing a year, without applying the brand [?] of the royal house to cattle which were not due to them, thereby increasing their number, and stealing that which was stamped from them. They went out from house to house, beating and plundering without leaving a hide for the people.
- Quoted in Breasted, Ancient Records of Egypt, Volume II
This division of the armies is hardly unsurprising, given the geography of Egypt. Dividing their forces into a northern and a southern contingent enabled Egypt to guard against any threat from Kushites to the south and also from whoever was the dominant Mesopotamian power of the day in the north.
These is some difficulty with the Nomes (or 'districts' or 'cantons' depending on one's preferences) listed by Herodotus, since many of the 42 Egyptian Nomes are not mentioned:
- Image source Wikimedia
It is possible that some Nomes were exempted from providing troops or, perhaps more likely, that Herodotus was unfamiliar with the system of Nomes - having probably never actually visited Egypt - and so only listed the ones that he was aware of.
As for the Medjay, the last mention of the Medjay is during the Twentieth Dynasty (1189-1077 BCE). As the Wikipedia article you cited notes,
"It is unknown whether the Medjay as an occupation had been abolished or the name of the force had changed".
Herodotus makes no suggestion that the Medjay were in any way related to the Hermotybians and Calascirians (or Calasiries and Hermotybies, depending on the translation of 'Histories' you have available). This is hardly surprising, since Herodotus wasn't even born until 485 BCE, fully six centuries after the Medjay were last mentioned in the actual records of Ancient Egypt.