We have a lot on male-on-male flirting here: http://www2.adult-fanfiction.org/forum/index.php/topic/17245-men-flirting-with-men/
I'm not a native speaker, but my two cents are thus:
Charmer: Someone who is either innately charming (possibly without realising it) or who knows what to say and do to charm people effectively. Not necessarily inclined to use this ability for sex, more likely to be applied to his business (actor, reporter, any position where a sale takes place). Usually charmers are confident people who seem to know what they're doing (innate leaders) and/or extremely good at making people feel comfortable, seeming trustworthy and putting them at ease.
Playboy: May not necessarily be charming (might get by on looks or wealth alone), but (assuming you are using the modern definition) is out to get as much tail as he can. The old definition merely denotes a wealthy, usually good-looking, man who doesn't have a regular job, therefore all the time in the world to "play." This used to mean sports, gambling, races, travelling and a cavalcade of leisure activities, but nowadays the "play" bit usually means sex.
If you want to explore the interactions between a charmer and a playboy, it'd be interesting to see them compete, at first, in a sense. If they are the emblems of two opposing causes (like tearing down a historical building to build a mall vs. those who want to preserve the old ruin), then a competition to see who sways more people to their side would let you highlight the differences between their "styles." The charmer would be all about personal interaction. They would sit with the other person, one-on-one, and explain their proposal. By the time they're done, very few would be unconvinced. The playboy would just waltz around and just ask people to sign a paper or support their cause, convinced that their looks and reputation will see them through, just as they have done every single time.
And as an extra advice: It's okay not to jump straight into the flirting/sexual arena. It's okay, in a story, to set the mood beforehand, to show us how the individuals go about their lives before they even meet at all. A foil is a piece of black cloth on which jewels and gems are placed on in order to bring up their colour and shine. If the flirting and sexual interactions are the gems, the moments where the characters are alone or with other people are the foil. They may not be as important to the story as you think, but they help you make the interactions between the main character more intense and interesting, by virtue of simple contrast.
Food for thought.
Apollo: Ha. Ha. Ha. Old predictable me, eh?