I'm not sure if he has a Zoolander-style name for that look but I imagine it would be called the "Punch Magnet." I assume this is the trademarked charming smile that he uses to melt ladies' hearts and tickle the money out of their wallets at the box office. This makes no sense.
As far as corner-of-the-mouth smiles go, there's one that says, "I'm a loveable rogue and you just never know what I might do next!" and there is one that says, "I guess you saw through my tough outer shell to the sensitive guy deep down." He doesn't do either of those. What we have here is the "I've got a bridge I want to sell you" smile. Or in the context of his movies, "I'm going to tell you a bunch of lies so I can have sex with you."
"Like new. Hardly been driven. Have sex with me."
Some people think women like being lied to and mistreated by "alpha male" types, but these are generally people who study women only by reading books and being rejected. A lot of women enjoy some level of mischief and roguishness in a man, but not the level that would ditch them without a callback number and leave gifts such as a pregnancy, an STD or the privilege of being an entry in a book of "conquests." The thought of that is not usually appealing to a woman when being picked up on, because I guess women are just crazy.