There are several words in Greek that mean both "holiness" and "sanctification". One of those is ἁγιασμός (hagiasmos). It's mostly used by Paul in his letters, but is also used in Hebrews 12:14 and 1 Peter 1:2. Paul uses it in Romans 6:18; 22; 1 Corinthians 1:30; 1 Thessalonians 4:3; 7; 2 Thessalonians 2:13; and 1 Timothy 2:15. BDAG defines this as "personal dedication to the interests of the deity, holiness, consecration, sanctification; the use in a moral sense for a process or, more often, its result (the state of being made holy) is peculiar to our lit. (New Testament).” So, depending on the context, ἁγιασμός either relates to the process that Christians go through during their lives, or the initial "setting apart" at conversion/infilling of the Holy Spirit. I suppose we could assign either "holiness" or "sanctification" to the context. Here is an example of how I translated 1 Thessalonians 4:3-8:
3 For this is God’s will, your sanctification, for you to abstain from sexual immorality; 4 that each of you should learn to master his own vessel in holiness and honor, 5 not in lustful desires as the Gentiles do, who don’t know God; 6 not to overstep and to take advantage of his brother or sister in the task, because the Lord is the avenger concerning all of these things, just as we also spoke to you beforehand and declare solemnly. 7 For God didn’t call us in impurity, but in holiness. 8 For that very reason, the one who rejects this instruction does not reject man, but God who [also] has given his Holy Spirit into you.
In verse three, the context refers to the “process” and in verse 7, I interpreted the use as the initial experience. Of course, others could interpret this differently.