"Aristarchus my fellow prisoner greets you, and Mark the cousin of Barnabas (concerning whom you have received instructions - if he comes to you, welcome him)," - Colossians 4:10 ESV
Both of these men were famous is their own way. Aristarchus traveled with Paul.
"So the city was filled with the confusion, and they rushed together into the theater, dragging with them Gaius and Aristarchus, Macedonians who were Paul's companions in travel." - Acts 19:29 ESV
"Sopater the Berean, son of Pyrrhus, accompanied him; and of the Thessalonians, Aristarchus and Secundus; and Gaius of Derbe, and Timothy; and the Asians, Tychicus and Trophimus." - Acts 20:4 ESV
"And embarking in a ship of Adramyttium, which was about to sail to the ports along the coast of Asia, we put to sea, accompanied by Aristarchus, a Macedonian from Thessalonica." - Acts 27:2 ESV
It seems that this man was a man 'outside' who worked and saw to Paul's needs in prison. Paul calls him a fellow prisoner and perhaps he was in a literal sense but it seems that he was voluntarily limiting himself by taking on a ministry to visit the prison and care for Paul. He was likely known by the early Church because of his exploits with Paul.
John Mark was also known but in a different way. He was likely seen by some as infamous.
"And Barnabas and Saul returned from Jerusalem when they had completed their service, bringing with them John, whose other name was Mark." - Acts 12:25 ESV
"When they arrived at Salamis, they proclaimed the word of God in the synagogues of the Jews. And they had John to assist them... Now Paul and his companions set sail from Paphos and came to Perga in Pamphylia. And John left them and returned to Jerusalem," - Acts 13:5, 13 ESV
"And there arose a sharp disagreement, so that they separated from each other. Barnabas took Mark with him and sailed away to Cyprus," - Acts 15:39 ESV
He also had exploits but at a certain point he left Paul on the field and Paul and Barnabus had a falling out that involved this man. He later becomes very dear to Paul. He calls him a son (see 1 Peter 5:13) and very useful (see 2 Timothy 4:11) but people are known to amplify failure and exhibit loyalty in the wrong ways.
"...and Mark the cousin of Barnabas (concerning whom you have received instructions - if he comes to you, welcome him)" - Colossians 4:10b ESV
You might say, 'Aren't we supposed to welcome everyone anyway?' No. Actually, we aren't. False teachers shouldn't be welcomed.
"If anyone comes to you and does not bring this teaching, do not receive him into your house or give him any greeting, for whoever greets him takes part in his wicked works." - 2 John 1:10-11 ESV
This welcome and greeting are the same idea. It didn't just mean, 'Say hello.' it meant invite into your home or invite to teach.
John Mark wasn't just talking the talk. He was walking the walk. Traveling with Paul was no picnic. Riots and stonings were not uncommon on those trips.
The man made some very public mistakes and perhaps Paul makes this clear statement to counteract people's common tendencies to see people after their mistakes.
God, please make us wise about who we greet. We never want to amplify failure and let it color our perceptions. We want honor and dignity to be the center of our expressions. Not the sentimental kind that honors because of renown but the genuine love and respect that originates in You and You alone.