The day of the Lord is the time of God's wrath. The coming of Jesus for his own is an entirely different event.
But related. The rapture is in 1Thessalonians4:15-18. Paul continues in 1Thessalonians5 to indicate when. Before the Day of the Lord begins.
The rapture is in 1Thessalonians5:10.
Verse 1 of the times and the seasons - for the resurrection/rapture, Paul just revealed. The world is going to be saying Peace and Safety. Which will be because they think they have entered the messianic age. But sudden destruction comes upon them - because the Day of the Lord hits them like a thief in the night. Which a person can go to 2Thessalonians2:3-4, the Day of the Lord is triggered by the person, their thought-to-be messiah, goes into the temple, sits, claims to be God.
They shall not escape. Just the opposite which Jesus said to believers in Luke 21:34-36 - to escape and stand before the Son of Man. Jesus said to be sober, just as Paul said below.
In verse 9, not appointed to wrath. Verse 10, whether asleep (the resurrection) or wake (the rapture), we should live with Jesus forever... escaping to heaven the Day of the Lord, its beginning, here on earth which will come upon all them that dwell upon the face of the whole earth (Luke 21:35) .
1 But of the times and the seasons, brethren, ye have no need that I write unto you.
2 For yourselves know perfectly that the day of the Lord so cometh as a thief in the night.
3 For when they shall say, Peace and safety; then sudden destruction cometh upon them, as travail upon a woman with child; and they shall not escape.
4 But ye, brethren, are not in darkness, that that day should overtake you as a thief.
5 Ye are all the children of light, and the children of the day: we are not of the night, nor of darkness.
6 Therefore let us not sleep, as
do others; but let us watch and be sober.
7 For they that sleep sleep in the night; and they that be drunken are drunken in the night.
8 But let us, who are of the day, be sober, putting on the breastplate of faith and love; and for an helmet, the hope of salvation.
9 For God hath not appointed us to wrath, but to obtain salvation by our Lord Jesus Christ,
10 Who died for us, that, whether we wake or sleep, we should live together with him.