What does it mean to be cast out from the presence of God, and what does it mean to be in the presence of the holy angel and the Lamb?
How can I explain the difference to someone who thinks Revelation 14:10 contradicts 2 Thessalonians 1:9?
In light of your question why one is cast out from the presence of the Lord and another one is in His presence Being tortured has to do with different judgments.
Throughout Scripture one can see God Gods judgments are different depending on how much light has been revealed to a people, nation or just one person.
Here are a few examples.
Woe to you, Chorazin! Woe to you, Bethsaida! For if the miracles that were performed in you had been performed in Tyre and Sidon, they would have repented long ago, sitting in sackcloth and ashes. 14But it will be more bearable for Tyre and Sidon at the judgment than for you. 15And you, Capernaum, will you be lifted to the heavens? No, you will go down to Hades.
Here's a little more information on the people who were eventually banned from the Lord's presence.
Acts 17:1-14 Talks about these people who will eventually have their judgment.
They were causing much suffering to the believers in Thessalonica as well as other places Paul went. According to Scripture Jews wanted to be in the kingdom when their Messiah comes.
But because they were persecuting the true believers of the Messiah this is what the verdict was.
2 Thessalonians 1:9
Who shall suffer justice — destruction age-during — from the face of the Lord, and from the glory of his strength, when He may come to be glorified in his saints,
The saints who suffered In Thessalonica will be glorified and those who persecuted them will see the truth and will they will shut out from the presence of the Lord.
The other judgment in Revelation 14:10 Is very severe because of all the supernatural things that will be taking place at that time. Even another gospel will be proclaimed by an angel just for the people on the earth at that time… It will be given to all tribes, people and languages.
And I saw another messenger flying in mid-heaven, having good news age-during to proclaim to those dwelling upon the earth, and to every nation, and tribe, and tongue, and people, saying in a great voice, ‘Fear ye God, and give to Him glory, because come did the hour of His judgment, and bow ye before Him who did make the heaven, and the land, and sea, and fountains of waters.
God always warn's people before he brings
a specific judgmenton at that time.
So here's the judgment that follows those who do not obey the angels message and in turn end up bowing down to the beast.
n a loud voice, “If anyone worships the beast and its image, and receives its mark on his forehead or on his hand, 10he too will drink the wine of God’s anger, poured undiluted into the cup of His wrath. And he will be tormented in fire and sulfur in the presence of the holy angels and of the Lamb. 11And the smoke of their torment rises forever and ever. Day and night there is no rest for those who worship the beast and its image, or for anyone who receives the mark of its name.”
That is the context that has Verse 10 in it.
And he will be tormented in fire and sulfur in the presence of the holy angels and of the Lamb.
One group is being banished from the Lord's presence and the other one is being tortured in front of the Lamb.
It's also interesting they are being tortured in front of the Lamb instead of the Lord. Two different titles.