The other is a straight-laced, quiet-living 27-year-old boy from Dunblane, whose idea of downtime from his profession tends to be watching more sport on TV, going for walks with his dogs Maggie and Rusty or playing yet more sport on his Playstation. But it hasn't taken long for Amelie Mauresmo and Andy Murray to unearth some common ground. It is located at Arsenal's Emirates Stadium as well as Wimbledon's Centre Court.
Some time spent in Mauresmo's company last week as the days ticked down to the start of Wimbledon offered a rare insight into areas of convergence and compatibility in the latest unlikely pairing in world tennis. In this World Cup year, football is as good a place as any to start. As a child, Mauresmo dreamed of playing the sport professionally, and today the pair share an appreciation of Arsenal and Arsene Wenger.
Next on Mauresmo's list, she jokes, is introducing the tee-total Scot to the merits of Bordeaux and Beaujolais.
"Right now there is a lot of football going on, so there are a lot of chats about football," said Mauresmo. "I follow it a little bit, although I'm not crazy about it anymore, like I used to be. He likes them [Arsenal] more than me actually. We talk some more about tennis for now but we chat. He doesn't like wine so ... I'll have to teach him. But not now."
While football is the ice-breaker as Mauresmo engages with the Scot's extended entourage of Dani Vallverdu and fitness trainers Matt Little and Jez Green, overcoming one's fears is another topic that crops up in the more intimate conversations she shares with the Scot, such as the one which took place over dinner on Wednesday evening. Despite being world No 1, Mauresmo had to master her moods to fight off the tag of being a serial choker, but she also knows the thrill of attempting to defend a Wimbledon title after winning it in 2006.
Mauresmo's career ended with just two major wins and a nagging feeling that she could have done more but for the nerves which particularly seemed to afflict her at her home Grand Slam of Roland Garros. Murray, a student of the game who has no intention of succumbing to such a fate, soaks up such details like a sponge.
"It was interesting to share these feelings and maybe help him try to avoid negative thoughts," said Mauresmo. "Although I think he is handling pressure really well, with the results he's had at Wimbledon over the past few years. He's already impressive. But he's curious, always asking questions and we're able to share. It's good.
"As I remember it, it feels great to defend a Wimbledon title. Pressure I think is less important now that he's won last year. It's pure joy I would say. And of course, there is the goal of winning again and focusing on the game and what to do on the court. But I feel first of all it's joy and being so proud to be there to defend the title."
Mauresmo has had her fair share of criticism and derogatory comments to contend with, even when she was playing (Wimbledon finalist Lindsay Davenport said that taking her on was like "playing a guy", and Martina Hingis called her "half a man") so she is not fazed by the sceptical reaction in some quarters to her appointment as Murray's coach.
"To be honest I didn't read anything, to start with," she said. "But I am not surprised. On this subject, what I said from the beginning was that I am happy if Andy having this open mind can help things change and move a little bit. I would be really happy about this. But it's not my main concern. My main concern is to really help Andy the best way that I can in this short time that we have before Wimbledon."
After coming out as being gay in a blaze of publicity in November 2006 - she always felt the way it was handled was clumsy and stage-managed - Mauresmo has learned to trust her instincts. Such an approach has served her well in her previous coaching stints, with Michael Llodra in 2010, Victoria Azarenka in 2012, and Marion Bartoli's Wimbledon triumph in 2013, and that is how she will approach this partnership too. She has resisted the chance to speak to her predecessor Ivan Lendl prior to the tournament and in truth her methodology couldn't be more different: she will feel no compulsion to mimic the taciturn Czech's demeanour in the players' box.
"I really want to enter this new experience with my own eyes and have my own idea of the things that are going on, how Andy is, how everyone is," she said. "Maybe I will do it later but at the moment I don't see it this way.
"My way is really instinctive. I guess you need a little time to get to know everyone. To get to know Andy of course, but also the people around him. I have taken it in a really natural way. That's how I take things in general. I approach it quietly and slowly to find my spot in this team.
"It's tough to compare Ivan and me - I don't think I have to sit up straight [in the players' box]. We are so different ... in every way. I don't know Ivan very well. I only know him through Andy's eyes and I don't think I will bring the same as Ivan. Which is good. Maybe I can bring him different things."
There is an acknowledgement from all concerned that the timing is difficult. While Mauresmo watched the Scot's two matches at Queen's Club, they have only had a week of practice together at Wimbledon, a period where she has gradually moved from the role of observer to participant. Her modus operandi is not to reinvent the wheel during practice sessions, nor fundamentally alter the principles which have served Murray so well.
"A couple more weeks would have been really good," she said. "But it is fine. It's exciting, for both of us I think, but certainly for me. I needed those few days. He had to play matches so I really didn't want to disturb any of his routine and the things he likes to do.
"His DNA is not going to change drastically. He knows how to play on every surface but on grass, playing the final in 2012, winning the Olympics, winning last year, he knows how to do this stuff so maybe I'm trying to add little things here and there but the timing is difficult.
"I'm not going to invent any new fancy drills and Andy knows that. What I did with both Marion and Vika was more about the game, how to play, but also how to approach it, approach the moment, approach competitions, and with Marion last year, approach the length of the Grand Slam. But Andy knows that pretty well already."
Murray begins the defence of his title against David Goffin tomorrow, but although results will not define the length of this partnership, ultimately Mauresmo accepts the arrangement will be deemed a failure if it cannot deliver further Grand Slam victories. "The final goal is this, that is for sure," she said. "If it can happen in a couple of weeks, great. But pressure is big. It would be great to win. But every tournament, after Wimbledon he will also want to win. I have my fingers crossed."