First, "A bit different" is a gross understatement. Hillary Clinton and Ted Cruz share nothing in common when it comes to matters of foreign policy, either in their beliefs or approach. You keep trying to draw this line, and it makes no sense. There's a huge difference in what they're advocating, even if they could both describe it as "smart power." One actually is smart power, if for no other reason than she's not advocating "precise" carpet bombing...whatever the hell that is.
And while I wouldn't call a person sexist for this, I do believe this is gendered thinking. As I said earlier, "hawkish" is a term I've mostly only seen applied to Hillary this entire election season, on both sides. Bernie has openly stated he would use military force, even increased military force, if he had to as a last resort (which is what Hillary has said). Cruz, Kasich, and Rubio were openly calling for a vastly increased military presence to fight ISIS, with Kasich going a step further and calling for boots on the ground in several countries. Hillary Clinton, on the other hand, basically wants to continue what Obama is already doing. So why does it seem like she has ownership of the term hawkish, when what she has called for has been mild and support-focused at its most extreme? Personally, I do think it's because she's a woman. She's woman who's not afraid to be tough, who won't be foolish and completely take the use of military force off the table if asked even while strongly favoring diplomacy and force used only as a last resort and, unlike most of the field, she's intelligent and experienced enough to go into hair-splitting detail when questioned. Lets not pretend that we as a society haven't had issues with women like this before. And for this, she gets called a hawk.