These gifts are presents for the bride, different from the bride price which is for the family.
Today in the U.S., this would be like the engagement ring, or wedding ring.

Eliser gives gifts of gold to Rebekah at the well.

Genesis 24:22 And it came to pass, as the camels had done drinking, that the man took a golden earring of half a shekel weight, and two bracelets for her hands of ten shekels weight of gold;

Eliser gives more gifts later to her family, which are the dowry.

Genesis 24:53 And the servant brought forth jewels of silver, and jewels of gold, and raiment, and gave them to Rebekah: he gave also to her brother and to her mother precious things.

Gifts are given in addition to the dowry.  They are mentioned as two things in the story of Haman and Dinah.

Genesis 34:12  Ask me never so much dowry and gift, and I will give according as ye shall say unto me: but give me the damsel to wife.

Numbers 18:6  And I, behold, I have taken your brethren the Levites from among the children of Israel: to you they are given as a gift for the LORD, to do the service of the tabernacle of the congregation.

And Gifts given to the people at Esther's wedding:

Esther 2:18  Then the king made a great feast unto all his princes and his servants, even Esther's feast; and he made a release to the provinces, and gave gifts, according to the state of the king.

The Gifts to the bride of Christ are the spiritual gifts of the Holy Spirit.

John 14:
26 But the Comforter, which is the Holy Ghost, whom the Father will send in my name, he shall teach you all things, and bring all things to your remembrance, whatsoever I have said unto you.
27 Peace I leave with you, my peace I give unto you: not as the world giveth, give I unto you. Let not your heart be troubled, neither let it be afraid.

Matthew 7:11  If ye then, being evil, know how to give good gifts unto your children, how much more shall your Father which is in heaven give good things to them that ask him?

Luke 11:13 If ye then, being evil, know how to give good gifts unto your children: how much more shall your heavenly Father give the Holy Spirit to them that ask him?

Acts 8:20  But Peter said unto him, Thy money perish with thee, because thou hast thought that the gift of God may be
purchased with money.

Romans 5:
15  But not as the offence, so also is the free gift. For if through the offence of one many be dead, much more the grace of God, and the gift by grace, which is by one man, Jesus Christ, hath abounded unto many.
16 And not as it was by one that sinned, so is the gift: for the judgment was by one to condemnation, but the free gift is of many offences unto justification.
17 For if by one man's offence death reigned by one; much more they which receive abundance of grace and of the gift of righteousness shall reign in life by one, Jesus Christ.)
18  Therefore as by the offence of one judgment came upon all men to condemnation; even so by the righteousness of one the free gift came upon all men unto justification of life.

1 Corinthians 2:9 But as it is written, Eye hath not seen, nor ear heard, neither have entered into the heart of man, the things which God hath prepared for them that love him.

1 Corinthians 7:7  For I would that all men were even as I myself. But every man hath his proper gift of God, one after this manner, and another after that.

1 Corinthians 12:4 Now there are diversities of gifts, but the same Spirit.

1 Corinthians 14:1 Follow after charity, and desire spiritual gifts, but rather that ye may prophesy.

1 Corinthians 14:12 Even so ye, forasmuch as ye are zealous of spiritual gifts, seek that ye may excel to the edifying of the church.

2 Corinthians 1
21 Now he which stablisheth us with you in Christ, and hath anointed us, is God;
22 Who hath also sealed us, and given the earnest of the Spirit in our hearts.

Ephesians 2:8  For by grace are ye saved through faith; and that not of yourselves: it is the gift of God:

Ephesians 4
7 But unto every one of us is given grace according to the measure of the gift of Christ.
8 Wherefore he saith, When he ascended up on high, he led captivity captive, and gave gifts unto men.

James 1:17 Every good gift and every perfect gift is from above, and cometh down from the Father of lights, with
whom is no variableness, neither shadow of turning.