Most Helpful Girl
'Bad boy' would be different to 'asshole'.
The whole idea of the bad boy in romance books is that this is a tough guy with this soft heart to him and it makes a girl feel special that she's the one that gets to tap into that. You'll also notice that in most romance novels or films, the 'bad boy' gets emotionally wrecked at some point because of how he feels for the girl - it's an element of power for the female viewers, to know that they can have that much hold over someone.
So basically a bad boy is someone who seems tough but cracks for the right person and obviously that makes girls feel special. Not really my thing, I'd prefer someone who's nice all the time rather than to just me but hey, I can understand why it's such a popular trope.
A bad boy is different to an asshole because the asshole is just a dick pretending to be a bad boy. Bad boys have a kind vulnerable personality deep down that they're covering up, assholes are just bad people.