((servant G1401)) - doulos
1 Corinthians 7:21-23 21 Are you called being a servant (G1401)? care not for it: but if you may be made free, use it rather. 22 For he that is called in the Lord, being a servant (G1401), is the Lord's freeman: likewise also he that is called, being free, is Christ's servant (G1401). 23 You are bought with a price; be not you the servants (G1401) of men.
John 8:34-36 34 Jesus answered them, Verily, verily, I say unto you, Whosoever commits sin is the servant (G1401) of sin. 35 And the servant (G1401) abides not in the house for ever: but the Son abides ever. 36 If the Son therefore shall make you free (G1659), you shall be free indeed.
"A “doulos” is a bondservant or slave. It means one who has given himself up to another’s will, disregarding his own interests and desires." - KHRM
((bondage=servitude G1402)) - douloo
((make free=set at liberty G1659)) - eleutheroō
Being under bondage is contrasted with being set free. So it would follow that being not under bondage would be likened to the same, that is, being set free.
Romans 6:18 Being then made free (G1659) from sin, you became the servants* (G1402) of righteousness.
*you were brought under bondage/to servitude to righteousness
Romans 6:22 But now being made free (G1659) from sin, and become servants* (G1402) to God, you have your fruit unto holiness, and the end everlasting life.
*and brought under bondage/to servitude to God
1 Corinthians 7:15 But if the unbelieving depart, let him depart. A brother or a sister is not under bondage (G1402) in such cases: but God has called us to peace.
not under bondage = not in servitude = not subjected/submitted to = not a servant of
Regardless of cultural/historical or modern connotations, bondage implies subjection to an domineering authority, either by coercion or willingly (e.g. taking upon oneself the yoke that is easy and the burden that is light - Matthew 11:29-30). It follows that being not under bondage implies the breaking of an existing yoke, as applicable.
It is easy for believers to see an application to marriage in being equally or unequally yoked, but not when said yoke is said to be broken by the unbeliever.
((depart=separate/put asunder G5563)) - chōrizo
Mark 10:7-9 7
For this cause shall a man leave his father and mother, and cleave to his wife; 8 And they two shall be one flesh: so then they are no more two, but one flesh. 9 What therefore God has joined together, let not man put asunder (G5563).
It does not mean separation cannot occur. But God commands that no separation be made to occur between two that He has joined together. It may be the case that an unbelieving spouse who is not subject to the law of God (Romans 8:7) separates (G5563) from the believing spouse (1 Corinthians 7:15).
1 Corinthians 7:10-11
10 And unto the married I command, yet not I, but the Lord, Let not the wife depart=separate (G5563) from her husband: 11 But and if she depart=separate (G5563), let her remain unmarried, or be reconciled to her husband: and let not the husband put away his wife.
Here again, there is not an indication that separation cannot occur. But God commands here that no separation be made to occur between a husband and his wife.
The departure/separation/putting asunder (G5563) by the believing wife does not cause her to cease to be her husband's wife. Indeed she is as long as he lives. She is called to be reconciled to the man who is her husband still according to God’s law (1 Corinthians 7:39; Romans 7:1-4).
1 Corinthians 7:15
But if the unbelieving depart (G5563), let him depart (G5563). A brother or a sister is not under bondage in such cases: but God has called us to peace.
What is commanded for the believing wife departing/separating (to remain unmarried (not remarry), for she indeed is married to a man, and to be reconciled to her husband) cannot be applied to the unbelieving wife departing for instance. In fact, the unbelieving person cannot "hear" the law by his/her very nature. Hence here are two different situations calling for two different handlings of the word of truth.
If the unbelieving departs/separates (G5563), there is no "word" for that person (1 Corinthians 5:12-13 applies?). The word is for the brother or sister. And the unbeliever has broken the yoke that joined the two.
Now bigger questions: Did, does or would God join two so that the result is an unequal yoke to begin with? What does "What therefore God has joined together" (Mark 10:9) imply that He joined together? Does God take pleasure in the making of ungodly soul ties? What the church has to deal with is equal yokes in ungodliness becoming unequal yokes with respect to godliness when one of two married persons comes to the faith in Messiah and so switches masters – I speak of blood-bought souls added to the church, not the professing Christian mess. I believe that is the exclusive situation that 1 Corinthians 7:15 is addressing.
What's a yoke?
"According to Vine's Bible Dictionary, the term yoke means "serving to couple two things together". In another Bible dictionary, it is defined as a coupling instrument that symbolizes forced labor, submission, and oppression driven by a higher power in authority. This definition is illustrated in the image below with two oxen that have been coupled together and are used for labor. If you take a closer look at the image you can see that the yoke is around the necks of the oxen. They are not joined by their tails, midsection, nor any other part of their anatomy. The weight of the yoke that surrounds their neck is supported by their shoulders."
"A yoke placed by the enemy is designed to destroy your life. That's why Jesus said that He came that we might have life and to have life more abundantly. The enemy's yoke will have you depressed, worried, stressed, confused, bitter, lying, stealing, fornicating, thinking suicidal thoughts, and a whole list of other things to keep you yoked to him. If you had all of this on your shoulders, you wouldn't be able to walk upright spiritually. To be coupled with the enemy is to share in his pleasures and his pleasure is to ultimately have you destroyed. He doesn't just want your life to end here on earth; he wants your life, meaning your soul, to be in eternal damnation with him."