Definition for the word vow – AI answer.
Yes, a vow is a form of swearing, but they are often used to describe different contexts.

Definition of “Swear” in the Bible.
Swear = G3660 ὀμνύω omnuo (om-noo’-o) v.
1. to swear, i.e. take (or declare on) oath
[a prolonged form of a primary, but obsolete omo, for which another prolonged form omoo om-o’-o is used in certain tenses]
KJV: swear

IT WAS NOT SIN TO VOW UNDER THE OLD COVENANT.

Under the old covenant, there were some instructions that were changed in the new covenant, and the keeping/making of vows unto God was one of them. Here is a reference to a vow about money/payment.  
(Eccl 5:4 [KJV])
When thou vowest a vow unto God, defer not to pay it; for he hath no pleasure in fools: pay that which thou hast vowed.

IT IS NOW SIN TO VOW UNDER THE NEW COVENANT.

Under the NEW COVENANT, we are commanded not to vow/swear/oath anymore.

Note: “Them of old time” refers to the Torah and or the prophets (Ecclesiastes).

(Matt 5:33-34 [KJV])
Again, ye have heard that it hath been said by them of old time, Thou shalt not forswear thyself, but shalt perform unto the Lord thine oaths: 34 But I say unto you, SWEAR NOT AT ALL; neither by heaven; for it is God’s throne:

Get this. In the new covenant, if you swear/vow/oath to anyone in God, IT IS NOW SIN. Again, under the New Covenant, swearing/vows/oaths made in God’s name should not be done. 

THE SIN AGAINST GOD IN TODAY’S MARRIAGES.

Every “Christian” marriage in this broken world sins in the face of God when the couple pronounces their vows/swearing/oaths in His name. See examples. 

Here is a simple vow (simple but deadly – transgression of God’s word/law is death).
“Before God and these witnesses, I vow to love, honor, and keep thee, in all faith and truth, as long as we both shall live.”

TTGM likes this one in particular – satan’s plug for one man and one wife.
“forsaking all others (women), till death do us part, according to God’s holy ordinance; and thereto I pledge thee my faith.”

THE WAY IT SHOULD BE DONE. 

TTGM makes agreements/covenants, but we do not vow/swear/oath to God like people do during a marriage. We say yes to this and no to that; that is all we do. Our word yes/no is good; we do not lie. Our King instructs us: read. 

(Matt 5:37 [KJV])
But let your communication be, Yea, yea; Nay, nay: for whatsoever is more than these cometh of EVIL.

DO NOT BE EVIL. 

What are you going to do about this sin? Consider the following. 
1. Speak to your pastor/priest about this sin.
2. At your next invitation to a wedding, are you going to partake in the sin by watching on with a smile?
3. Do you care if satan’s ungodly intentions continue in the lives of your family and friends? What is satan’s objective? To keep God’s people in sin/iniquity.
4. Do you not see why Yeshua died on the cross? For our sins. Yes, He died for our sins, and you are going to let ignorant people continue in sin without sharing what the word of God says?
5. Are you going to ignore the sin and continue to partake in this iniquity?

If you choose to ignore the sin, then join the Many; you will have your place.  

Be blessed in understanding. 

RELATED TOPIC:
God’s Way vs Man’s way 
Go Here to understand how sex/one flesh is marriage (Bible)
Read about the Many (to Hell) and the Few (to God’s Kingdom)
More about iniquity – The Many love iniquity.