Hidden and Manifest
The Rapture of the Church is a mystery. It's a secret coming of Jesus, and only His followers will see Him. Jesus will rapture His followers to protect them from the Great Tribulation and to take His bride.
"For the Lord Himself will descend from heaven with a shout, with the voice of an archangel, and with the trumpet of God. And the dead in Christ will rise first. Then we who are alive and remain shall be caught up together with them in the clouds to meet the Lord in the air. And thus we shall always be with the Lord." (1 Thessalonians 4:16-17)
The Rapture will take place in the blink of an eye. No one on Earth can see Jesus, and no one will know that Jesus is in the air. No man will see believers being caught up to the Father's house of God.
"In a moment, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, and the dead will be raised incorruptible, and we shall be changed." (1 Corinthians 15:52)
The emphasis of the Rapture of the Church is the meeting of Jesus with His followers. It is a joyous event where there is no mention of wrath or anger. This verse doesn't mention unbelievers; they are left behind and don't realize that Jesus has returned to take the believers.
During the Second Coming, Jesus will return to Earth, and all people will see Him appear. Jesus doesn't come for the believers; He comes to put an end to the reign of the wicked on Earth. Rather than the Bridegroom coming for His bride, it is the King and Warrior who will establish His kingdom on Earth. Everyone will see Him appear; it won't be an event that lasts less than a second.
"Behold, He is coming with clouds, and every eye will see Him, even they who pierced Him. And all the tribes of the earth will mourn because of Him. Even so, Amen." (Revelation 1:7)
"And I saw the beast, the kings of the earth, and their armies, gathered together to make war against Him (Jesus) who sat on the horse and against His army." (Revelation 19:19)