Not necessarily so: types, motifs and images are not essentially a single one-on-one correspondence.
You can compare this to "Israel", which can can mean one man, Jacob; or can mean the physical land of Israel (Ha'aretz Israel) or the *people* of Israel (Am Ha'aretz, people of the Land), or the 10 Northern Tribes, o uneducated country people (as contrasted tothe priestly and scribal classes), or even be extended to the whole Hebrew nation no matter were they live.
In a similar manner, "daughter of Jerusalem (or Zion)" can mean the actual physical, geographic territory of the capital city
Isaiah 16:1
" Send them forth, from Sela across the desert, to the mount of daughter Zion
Isaiah 10:32
Even today he will halt at Nob, he will shake his fist at the mount of daughter Zion, the hill of Jerusalem!
Or it can mean the haughty women of the city:
Isaiah 3:16
The Lord said: Because the daughters of Zion are haughty, and walk with necks outstretched, Ogling and mincing as they go, their anklets tinkling with every step
Or it can mean all the people of Israel:
Lamentations 2:1
How the Lord in his wrath has abhorred daughter Zion, Casting down from heaven to earth the glory of Israel, Not remembering his footstool on the day of his wrath!
Sometimes it means the military might of the nation. Look at Micah 4. In verse 10, God warns that the daughter of Zion will suffer as much as a woman in labor. But in verse 13, He promises vengeance. The weak, powerless woman will become a bull with horns of iron and hoofs of bronze that will crush its enemies: she represents the armed forces of the nation.
The thing to keep in mind is that in poetry, personifications are not often individual people and are images are never quite cemented in. They can be "types" that recur.
For instance, even the Beloved Woman in the Song of Songs can represent a favored member of Solomon's harem, OR his one beloved bride, OR the Church, OR the believer's loving soul, OR even the personification of the female warrior:
"Who is she who cometh forth, fair as the moon, bright as the sun, and terrible as an army with banners!" And as the Israel personification moves into the NT, the "Daughters of Jerusalem" may be Christ's female disciples, those who mourned HIm as He walked carrying His cross:
Luke 23:28
Jesus turned to them and said, Daughters of Jerusalem, do not weep for me; weep instead for yourselves and for your children
And in the end this female figure, Jerusalem, is none other than the Church!
Galatians 4:26
But the Jerusalem above is freeborn, and she is our mother.
Hebrews 12:22
No, you have approached Mount Zion and the city of the living God, the heavenly Jerusalem, and countless angels in festal gathering
Revelation 3:12
The victor I will make into a pillar in the temple of my God, and he will never leave it again. On him I will inscribe the name of my God and the name of the city of my God, the new Jerusalem, which comes down out of heaven from my God, as well as my new name.
Revelation 21:2
I also saw the holy city, a new Jerusalem, coming down out of heaven from God, prepared as a bride adorned for her husband. Daughter Zion -- isn't she beautiful!!
You DO like to QUOTE from James; right??
James 2:10
For whoever keeps the whole law and yet stumbles at just one point is guilty of breaking all of it.