In both accounts they involve the fact that the Lord Jesus will come...
The first one tells us that He will come as a thief in the night but that we as believers know this perfectly well and that that day of sudden destruction will not overtake us as a thief.
The second one gives different detail and mentions both His coming again as well as the believers' gathering together to Him ( what's called the "rapture" or catching away, see Matthew 24:29-31, Mark 13:24-27, Luke 21:27-28, and 1 Thessalonians 4:13-18 as examples ), and also tells us that there shall be a great falling away first and the man of sin / son of perdition ( damnation, also known as the "beast" or Anti-Christ of Revelation ) shall be revealed...
Sitting in the temple of God and attempting to shew that he is God ( the abomination of desolation, Daniel 9:27, Daniel 11:36-39, Matthew 24:15, Mark 13:14, Luke 21:20 ), speaking of the Anti-Christ which is yet to be revealed ( Revelation 13:1-8 ).
The Day of the Lord / the Day of Christ is the day that He comes...
Bringing with Him all of His saints as well as judgment upon those who do not know Him in the end of the days and of the kingdoms of this earth, before He takes over and rules all of them from Jerusalem for 1,000 years.
However,
I see that "the Lord's Day" referred to in Revelation 1:10 is known to us by many names, depending on what language or culture we come from....
In Spanish it is "Domingo", or "Lord's Day".
In French it is "Dimanche", same thing.
In English it is "Sunday" ( named after, of all things, the sun god ), and corresponds to the first day of the Hebrew 7 day week.
That is how I understand those terms and why, and I wish you well in your studies in His word.
May God bless you.