John Piper suggests a distinction in these two passages.
[Regarding] ...the presence of God in hell... there are two very relevant texts. Revelation 14:10, which gives the impression that the Lamb of God may be present in hell, says that those who worship the beast “will be tormented with fire and sulfur in the presence of the holy angels and in the presence of the Lamb.” And the other text is 2 Thessalonians 1:9: “They will suffer the punishment of eternal destruction, away from the presence of the Lord and from the glory of his might.”
So, first, a word about Revelation 14:10. When it refers to the torments of hell in the presence of the Lamb, the term “in the presence of” means “in the sight of,” not “in the same space as.” The Greek word used [enōpion] literally is “before the Lamb”; they will be tormented “before the Lamb.” The same word is used in Revelation 3:2 like this: “I have not found your works complete in the sight of my God.” That’s the same exact construction: “in the sight of my God,” “in the presence of my God.” He can see. It’s before him in that sense.
So when we say that something happens “in the sight of God” or “in the sight of the Lamb,” we don’t necessarily mean that God or the Lamb is in the same space of what they are seeing. So, I think Revelation 14:10 does not say that God or Jesus or the Lamb has some kind of ongoing residence in hell. But they can and do see hell.
Now, when 2 Thessalonians 1:9 says that the punishments of hell will be “away from the presence of the Lord,” the word for presence there [prosópon] is face, “away from the face of the Lord.” In other words, hell is a fulfillment of the threat in Ezekiel 7:22, for example, where God says, “I will turn my face from them.” It’s the exact opposite of the blessing in Numbers 6:24–26: "The Lord bless you and keep you; the Lord make his face to shine on you and be gracious to you; the Lord lift up his countenance upon you and give you peace."
That’s the exact opposite of what happens in hell. That does not happen in hell. The gracious countenance of God does not shine upon them. And there is in hell an everlasting frown of disapproving justice.