The Jews generally means anyone who belonged to the kingdom of Judah, and as Gesenius notes, in later times it was applied to any Israelite.
This can be seen in Nehemiah 1, where Nehemiah refers to the Jews interchangeably with the children of Israel:
1 The words of Nehemiah the son of Hachaliah.
It came to pass in the month of Chislev, in the twentieth year, as I was in Shushan the citadel, 2 that Hanani one of my brethren came with men from Judah; and I asked them concerning the Jews who had escaped, who had survived the captivity, and concerning Jerusalem. 3 And they said to me, “The survivors who are left from the captivity in the province are there in great distress and reproach. The wall of Jerusalem is also broken down, and its gates are burned with fire.”
4 So it was, when I heard these words, that I sat down and wept, and mourned for many days; I was fasting and praying before the God of heaven.
5 And I said: “I pray, Lord God of heaven, O great and awesome God, You who keep Your covenant and mercy with those who love You and observe Your commandments, 6 please let Your ear be attentive and Your eyes open, that You may hear the prayer of Your servant which I pray before You now, day and night, for the children of Israel Your servants, and confess the sins of the children of Israel which we have sinned against You. Both my father’s house and I have sinned.
-Nehemiah 1:1-6 (NKJV)
This does not necessarily exclude Jewish priests or nobles or rulers, since as you can see Nehemiah used the Jews in verse 2 to refer to all those who had escaped and survived the captivity.
However, the Jews and the children of Israel in Nehemiah several times contains the connotation of the common people of Israel in a more general sense.
When Sanballat the Horonite and Tobiah the Ammonite official heard of it, they were deeply disturbed that a man had come to seek the well-being of the children of Israel.
-Nehemiah 2:10 (NKJV)
Again, Nehemiah 2:10 does not necessarily exclude the Jewish priests, nobles, or rulers from being part of the children of Israel, but the sense is that someone had come to seek the good of all of Israel which consisted of a large majority of common people.
This would be similar to me saying "I have come to see to the well-being of the Brazilians." The sense would be that I am primarily referring to the common people of Brazil. I am not necessarily excluding any of the Brazilian leaders or clergy, but the connotation is mainly that of common Brazilians.
For the children of Israel and the children of Levi shall bring the offering of the grain, of the new wine and the oil, to the storerooms where the articles of the sanctuary are, where the priests who minister and the gatekeepers and the singers are; and we will not neglect the house of our God.
-Nehemiah 10:39 (NKJV)
But notice that here the children of Israel are distinguished from the children of Levi. The sense being that the common people and the priests would work together to make sure the house of God is not neglected.
And the officials did not know where I had gone or what I had done; I had not yet told the Jews, the priests, the nobles, the officials, or the others who did the work.
-Nehemiah 2:16 (NKJV)
Here the phrases are that Nehemiah had not yet told it
to the Jews / nor to the priests / nor to the nobles / nor to the rulers / nor to the rest that did the work. (KJV)
The sense is that
he had not told the Jews /
and [he had not told] the priests /
and [he had not told] the nobles /
and [he had not told] the rulers /
and [he had not told] the rest that did the work.
They cannot be taken as a parenthetical because they are additional specifications of whom Nehemiah did not tell. Nehemiah did not tell any of the common people, nor did he tell any of the more privileged people such as the priests, nobles, or officials, nor did he tell anyone who would later be directly involved in the work of restoring the walls. His intentions were initially kept from everyone, no matter what their position was.
Jews… priests… nobles… rulers — The various ranks and classes among the Jewish community. Nehemiah did not at that time make known his night journey around the walls to any one of these various classes. The Jews here means the common body of the people, the laity, as distinguished from the priests. The nobles were those who were known and honoured as descendants of the royal family of David. The rulers were the chief officers of the Jewish community living in and about Jerusalem.
Nor to the rest that did the work — The workmen among the people, as distinguished from the other classes previously mentioned. In every great public work such as Nehemiah was now contemplating, the builders, (Ezra 3:10,) and all classes of workmen, would have an important interest; yet Nehemiah means to say that while he held important papers from the king, and had come to build the walls and gates of Jerusalem, and made his night survey with this end in view, he had not as yet communicated his design to any of the people, nor to their officers and leading men, nor to the workmen upon whom would fall the chief burden of rebuilding the fallen gates and walls.
The priests, nobles, rulers, etc, being additional specifications and not part of a parenthetical, mirrors the first part of verse 16 when Nehemiah says
And the officials did not know where I had gone or what I had done; (NKJV)
Nehemiah says that they did not know where he had gone, and then adds an additional specification that they did not know what he had done.
The sense is that
[they did not know] where I had gone /
and [they did not know] what I had done;
Nehemiah 5 also distinguishes between Jews and rulers, Jews denoting the common people as opposed to the higher ranking rulers:
And at my table were one hundred and fifty Jews and rulers, besides those who came to us from the nations around us.
-Nehemiah 5:17 (NKJV)
Nehemiah 13:23 is using Jews in the same way. Nehemiah saw that some of the Jews had taken wives from Ashdod, Ammon, and Moab. 13:28 goes on to tell that a son of the high priest had even been involved in an unlawful marriage. The sins of the common people in verse 23 had crept into the priesthood so that even one of the high priest's sons partook in marrying a foreigner.