1 Thessalonians 4:13-18 describes the Rapture, when Christ comes to the clouds above the earth and catches up or raptures all living Christians on the earth to meet Him in the air. In Chapter 5 he changes topics. This is proven by his use of two little Greek words,
peri de. These two words in 1 Thessalonians 5:1 could be translated, "But concerning" or "Now about." These two words are used nine times by Paul in 1 Thessalonians and 1 Corinthians. Every time Paul uses these two words, they always denote a change in subject matter. In 1 Thessalonians 4:13-18 the subject matter is what happens at the Rapture. But in 1 Thessalonians 5:1-11 he introduces a new subject, a different event, the Day of the Lord. By doing this, Paul indicates that the Day of the Lord and the Rapture are not the same, they are separate events. That is, the events making up the Day of the Lord do not include the Rapture of the Church. But that's not all.
There are other reasons Paul gives why the events making up the Day of the Lord do not include the Rapture of the Church. What are they? We know from Zechariah 12 and 14 that the events making up the Day of the Lord include the nations gathering against Israel, great cosmic judgments that God brings, and the Day of the Lord ends with the Second Coming of Christ. But Paul tells Christians that they will not be overtaken by this Day of the Lord, that they are not a part of that day. Where does he say this? In 1 Thessalonians 5:4 he says, "But you, brethren, are not in darkness, that the Day should overtake you like a thief." Also, in verse 9 Paul tells them why they won?t experience any part of the coming Day of the Lord. He says, "For God has not destined us for wrath but for obtaining salvation through our Lord Jesus Christ." The Rapture is not part of the Day of the Lord, and takes place before it starts. How do we know this?
Paul told the Thessalonians in 1 Thessalonians 5:2, "For you yourselves have accurate [or perfect] knowledge about the day of the Lord." In other words, Paul is saying he had already given them full, exact information about the events that would happen during the Day of the Lord.
But it is interesting that even though they had perfect, accurate knowledge about the Day of the Lord, they were ignorant about the Rapture. In 1 Thessalonians 4:13-18, Paul tells them he does not want them to remain ignorant about the Rapture. Well, if they had perfect or accurate knowledge about the Day of the Lord but they were ignorant about the Rapture, then the Rapture must not be a part of the Day of the Lord or they would have known about it. So first, Paul writes about the Rapture in 1 Thessalonians 4, then he changes topics and writes Chapter 5 to calm their fears about the Day of the Lord. In doing so, he indicates that the Rapture of the Church will take place before the Day of the Lord starts. Since the Rapture is not part of the Day of the Lord, and since the Day of the Lord concludes with Christ?s returning to earth in judgment, the two events, the Rapture and the Second Coming, must be separate events.
The Day of the Lord is also mentioned as the Day of Christ in the King James within 2 Thessalonians 2. That time is marked by the middle of the Tribulation when the falling away of the saints takes place and the Antichrist shows himself to be God within the Jewish temple (i.e. the Abomination of Desolations). The Day of the Lord also lines up with sixth seal. Both events have blood moons and black dark skies. In other words, the Day of the Lord is a period of time. It is the the last half of the Tribulation which is a part of the Great Tribulation (that would include the killing of the saints by their refusing to take the Mark). The 6th seal is an answer of vengeance from the saints with the 5th seal in them crying out for justice (Because they were martyred by the Antichrist).
Source used for the reply on the transition made between 1 Thessalonians 4 and 1 Thessalonians 5:
Rapture Watch - a global end times prophecy resource.