The following contains spoilers from Punisher (2022) by Jason Aaron, Jesus Saiz and Paul Azaceta and Moon Knight (2021) by Jed Mackay and Alessandro Cappuccio.
The current comic book run of Punisher has revolutionized the character. From a revised origin story to leading the Hand, Frank Castle is now a very different man from who he was before the series, even if he is still doling out his own twisted version of justice. Some of the greatest elements of the series, however, has explored the mythology of the Hand and of Frank's own beliefs, including the fact that he does not truly believe in the mission of the criminal organization he is nominally leading.
As Frank gets further into the mythology of The Hand, he realizes that he is essentially the priest of a religion that he does not believe in. He is additionally referred to as the "fist" of the head of this religion. All of this terminology is familiar to fans of Moon Knight, and the similarities between the two go even further than that. Punisher and Moon Knight have consistently been two sides of the same coin, but their most recent runs make the characters far more similar than ever before.
Frank and Marc aren't unfamiliar with each other. Sometimes allies, sometimes enemies, the two often find themselves in the same area of crimefighting, regardless as to whether they want to be. Their first encounter was remarkably amicable in 1989's Punisher #2 by Mike Baron and Bill Reinhold. Nearly 30 years later, Punisher and Moon Knight traded taunts and insults in a now-memeified moment from Punisher (2018) #14 by Matthew Rosenberg, Szymon Kudranski and Antonio Fabela.
The two, even though intended as insults, essentially gave each other the measure of themselves. Marc thinks Frank is a murderer who is taking vengeance for something that should have ended long ago. Frank thinks Marc is crazy and serving an imaginary god. The two are actually operating on very similar levels, again trying to be good people while carrying out a higher mission that involves killing those who their source of morality deems guilty.
Punisher likely finds it necessary to recant his criticism to Moon Knight, as he just found out that he is also serving a dark god. What is more, he doesn't believe that the god whom he serves is a just and good being, nor does he believe in its being worthy of worship. However, he still carries out its will in order to save the world in his own way. This god has also given Frank powers which he has never known. These are powers which have been passed down to him from the previous "fists" of The Beast, which also echoes the powers that Hunter's Moon claimed were given to fists of Khonshu.
The two characters are incredibly similar in their most recent runs, and both of them attempting to make the best of a relationship with a god whom they don't really believe in is a very strange uniting factor. In spite of Moon Knight and Punisher often winding up on opposite sides ideologically (even as they fought together), the two share more than simple brutality now. Frank, as a sort of demigod of war, is preparing to put his powers to work against a god of war. Hunter's Moon just put his god to war against another, newer god. The two are going in very different directions: Frank is working for The Hand and Marc is trying to save his therapist. Their dissimilarities however, are becoming more sparse as the two develop.