The words used for people, peoples, nations in the Hebrew are these. עם "people" in the singular in general signifies Israel, עמים in the plural "peoples." This is very often indeed wrongly translated "people" in the Authorized Version, I suppose because "peoples" is not correct English; but the sense is quite different. I believe the עמים are the peoples in connection with Israel, brought into relationship with Israel. נוים on the contrary, are the nations in contrast with God's people. It is used of Israel, where it is disowned, in Psa. 43,חסיד- לא נוי an impious nation. There is another word, and quite general, לאכוים, "tribes," "races," and so "nations." This is the word translated people in Psalm 2, and often elsewhere. The word אמות is found in Gen. 25:16 (of Arab tribes), and in Num. 25:15, in the same sense. We have עמים in Psa. 18:47. In Psa. 3:6, it is עם Israel. In Psa. 7:8 it is עמות; that is, while a general word, not the nations looked at in contrast with Israel, "Gentiles," as we are accustomed to say. In Psa. 9 God is viewed as clearing the land of His enemies. He is known by the judgment He executes. The wicked (which may be of His people in the land) are turned into Sheol, are slain and go down into the pit, and the Gentiles also who give no heed to God but go their own way, despising Him. In Psa. 67:2, it is "all the nations" everywhere, contrasted with Israel who speaks. Verse 7 is the effect. In verse 3 they are looked at as brought into relationship, עמים. In verse 4 it is לאמים, all the various tribes of the earth. Then He judges them, not in destruction as נוים, but as peoples (עמים) under Him: then לאמים The various tribes or races He shall lead or govern. In verse 5 it is עמים all the various peoples, but viewed in relationship with Jehovah. We have in Luke 2. "before the face of all peoples." Were the λαοί expressed in Hebrew, it would be עמים a general word (not I think here לאמים) but viewed as brought into relationship with God. Then the nations, ἔθνη, (נוים) were viewed as wholly invisible, unseen and ignored. The light of Christ was to reveal them, bring them out into visible existence, so that they became עמים so to speak. Then "people Israel" is plain enough.
[1871.]