Foreword: Post writing this, I have come to the belief that God has both. The elect and the chosen. Proof? see here How do we have free will
These are referred to in scripture as Elect, Chosen, Beloved, Sheep, Children of Promise, Saints, Sons, Brethren, and the Sanctified.
Elect
(Isa 42:1) Behold my servant, whom I uphold, my chosen, in whom my soul delights; I have put my Spirit upon him; he will bring forth justice to the nations.
(Isa 45:5) I am the LORD, and there is no other, besides me there is no God; I equip you, though you do not know me,
(Isa 65:9) I will bring forth offspring from Jacob, and from Judah possessors of my mountains; my chosen shall possess it, and my servants shall dwell there.
(Isa 65:22) They shall not build and another inhabit; they shall not plant and another eat; for like the days of a tree shall the days of my people be, and my chosen shall long enjoy the work of their hands.
(Mat 24:24) For false christs and false prophets will arise and perform great signs and wonders, so as to lead astray, if possible, even the elect.
(Mat 24:31) And he will send out his angels with a loud trumpet call, and they will gather his elect from the four winds, from one end of heaven to the other.
(Mar 13:22) For false christs and false prophets will arise and perform signs and wonders, to lead astray, if possible, the elect.
(Mar 13:27) And then he will send out the angels and gather his elect from the four winds, from the ends of the earth to the ends of heaven.
(Luk 18:7) And will not God give justice to his elect, who cry to him day and night? Will he delay long over them?
(Rom 8:38) For I am sure that neither death nor life, nor angels nor rulers, nor things present nor things to come, nor powers,
(Rom 8:39) nor height nor depth, nor anything else in all creation, will be able to separate us from the love of God in Christ Jesus our Lord.
(Col 3:12) Put on then, as God's chosen ones, holy and beloved, compassionate hearts, kindness, humility, meekness, and patience,
(Col 3:13) bearing with one another and, if one has a complaint against another, forgiving each other; as the Lord has forgiven you, so you also must forgive.
(1Ti 5:21) In the presence of God and of Christ Jesus and of the elect angels I charge you to keep these rules without prejudging, doing nothing from partiality.
(Tit 1:1) Paul, a servant of God and an apostle of Jesus Christ, for the sake of the faith of God's elect and their knowledge of the truth, which accords with godliness,
(1Pe 1:1) Peter, an apostle of Jesus Christ, To those who are elect exiles of the dispersion in Pontus, Galatia, Cappadocia, Asia, and Bithynia,
(1Pe 2:6) For it stands in Scripture: "Behold, I am laying in Zion a stone, a cornerstone chosen and precious, and whoever believes in him will not be put to shame."
(2Jn 1:1) The elder to the elect lady and her children, whom I love in truth, and not only I, but also all who know the truth,
(2Jn 1:13) The children of your elect sister greet you.
Elected
(1Pe 5:13) She who is at Babylon, who is likewise chosen, sends you greetings, and so does Mark, my son.
(Act 13:48) And when the Gentiles heard this, they began rejoicing and glorifying the word of the Lord, and as many as were appointed to eternal life believed.
Election
(Rom 9:11) though they were not yet born and had done nothing either good or bad--in order that God's purpose of election might continue, not because of works but because of him who calls--
(Rom 11:5) So too at the present time there is a remnant, chosen by grace.
(Rom 11:7) What then? Israel failed to obtain what it was seeking. The elect obtained it, but the rest were hardened,
(Rom 11:28) As regards the gospel, they are enemies of God for your sake. But as regards election, they are beloved for the sake of their forefathers.
(1Th 1:4) For we know, brothers loved by God, that he has chosen you,
(2Pe 1:10) Therefore, brothers, be all the more diligent to make your calling and election sure, for if you practice these qualities you will never fall.
Elect’s
(Mat 24:22) And if those days had not been cut short, no human being would be saved. But for the sake of the elect those days will be cut short.
(2Ti 2:10) Therefore I endure everything for the sake of the elect, that they also may obtain the salvation that is in Christ Jesus with eternal glory.
(Mat 22:14) For many are called, but few are chosen."