The four designations are one and the same. The presence of Christ Jesus with His saints after the "Rapture" is the referred day (1st. Thessalonians 4:16,17).
The servant labors, holds forth the word of life so that there shall be children of God to rejoice over in the presence of Christ in that day.
2 Corinthians 1:14 Owing to the acknowledgment of the Corinthians that God had spoken to them in Paul there will be mutual rejoicing in the day of the Lord Jesus.
In the day of the Lord Jesus the believer is unimpeachable, for God is faithful in His calling. Of those who put their trust in Christ as Saviour, none shall be lost; therefore the laborer and the fruit of his labor will rejoice together in that day.
Thessalonians 2:1-6 The day of the Lord will begin when the Antichrist is revealed; whose coming is according to the working of Satan; but after the departure of the Christian saints to be with Christ.
The Christian is a child of Light, not of darkness, and will not be present when the day of the Lord comes as a thief in the night.
2 Peter 3:10 The "day" comes in as a thief and ends in the dissolution of the heavens and the earth which are now. A new heavens and a new earth will usher in "The Day of God."
Isaiah 2:12-21 Symbolically, the subjects of judgement in the day of the Lord are men (verses 12,13), governments (verse 14), the military (verse 15), commerce and art (verse 16), idolatry (verses 18,20). And for fear of the Lord men shall hide themselves in the dens and rocks of the mountains (Revelation 6:15,16).
Isaiah 13:6,9,13 The prophet Isaiah warns of the coming day of destruction. One nation will rise against another (verses 17,19), until a man becomes more precious than the golden wedge of Ophir
Isaiah 34:8 It is the day of the Lord's vengeance. This is the last mention of the day by Isaiah, and the remaining chapters record the blessings being prepared for Israel and the people of the nations that remain (Isaiah 52:6). The God of vengeance returns and is occupied with Israel, and the judgements are spoken of in the past tense. (Isa.63:4)
Ezekiel 13 Foolish prophets, wicked prophets, false prophets and ungodly sorceresses in the land in the day of the Lord.
Ezekiel 30:3,9,18 The past history of Egypt and Ethiopia is repeated in that day.
Joel 1:15-20 The destruction of the necessities of life is predicted (verses 1,2,11,15,31). The Lord leads an army (verse 11) of invaders which destroys the land: but deliverance shall be at Jerusalem and Mount Zion. A warning and a promise. (see Joel 3:14,18; Amos 5:18-20; 6:37; 9:11; Obadiah 15). The heathen come into remembrance for their abuse of helpless Israel and Judah.
Hosea 1:11 The gathering and uniting of Israel and Judah is accomplished in the day of the Lord.
Hosea 2:18-23 All nature rejoices and Israel is sown again in the earth. The covenant of God with the animal creation is fulfilled in that day (verse 18; Romans 8:19-22).