David Kelly: 'Gaffers' dinner date may thaw frostiness'
They share the same surname and occupy the same island, though they are largely viewed through starkly different prisms.
And yet there are occasions when it has been difficult to tell the difference. Or to muse sometimes about the merits of, perhaps, attempting to switch each O'Neill from one Ireland to the other.
Maybe nobody would notice. Or, indeed, care.
It is only two summers since Northern Ireland and the Republic of Ireland shared a major tournament platform for the first time since the partition of soccer in the early 1920s.
The graph for both has been steadily pointing downwards since then, Northern Ireland drifting into that sort of listless territory where it seems they can go decades without scoring a competitive goal.
The Republic, meanwhile, without any immediate prospect of rude health, have resorted to their occasional and typically southern, sepia-tinted optimism that things will come good again because, well, they always do.
It's a state of affairs which makes the on/off cordiality between the rival managers appear less of a virulent feud between top-ranked coaches, rather more two suburban dwellers quarrelling over some uncontrollable creeping ivy.
The example of Jimmy Dunne, a player who could sit in a McDonald's in Belfast or Dublin and remain quite unrecognised by even the most devoted soccer fan, is a case in point.
The tussle for his services is not so much a tug of war than it is the proverbial two bald men scrapping for a comb.
Michael met defender Dunne in Edinburgh last month - buying him a cappuccino - in the hope of persuading the Burnley player (on loan to Hearts) to pitch his lot in with the North.
Martin, who has never capped a player from the Scottish Premier League, was suitably roused by a 20-minute cameo for the U-21s to include him in his squad for this week's games, before informing the player that he would also be withdrawing him from the squad a few days later.
All of which would make one wonder what the atmosphere might be like as the managerial duo sat down in the Mansion House for the Co-Operation Ireland dinner last evening.
"I'm sure the president has more than a cappuccino laid on for me," smiles the former Shamrock Rovers manager, who feels Dunne now owes him a cappuccino too.
For his part, Martin, although miffed at a recent interview when his counterpart railed against suspected poaching of Northern-born Catholic players, seems satisfied that relations are cordial.
"I have no problem with him, I get on really fine with him, I think. Hopefully it's reciprocated, but I don't know."
Over to you, Michael.
"Everything's fine," he tells me. "I don't understand it.
"It's interesting for me that a lot was written about eligibility but we've packed the place out today with journalists who could have asked questions about it!"
He is being ironic, as the Irish Independent is the only media attendee from the Republic at the pre-match press conference, itself quite notable.
"There are no issues. We're both doing the job that we do. I'm looking forward to catching up tonight with Martin."
The two associations have also sought to build bridges - like some of the players from either side who visited Crumlin Children's Hospital on Thursday.
The joint bid for the European U-21 Championships reflects a sense that instead of working against each other, two football territories of limited resources are much better off working with each other.
Squabbles are inevitable and in Dunne's case, one senses it would be a pyrrhic victory whichever side claims his services.
Michael O'Neill will plough on; he remains a success story in straitened circumstances and a reminder that the much-maligned League of Ireland can propel managers, as well as players, into the international arena.
"It's much different because club football dictates your schedule. International football is different.
"And the other thing I found was having to step up and manage players on a different level to those I worked with at Shamrock Rovers.
"That would be a challenge Stephen (Kenny) would have. He has done an amazing job with Dundalk. For me he has certainly all the attributes to work outside of the league and international level as well."