From what I've gleaned through the almighty interwebs, the broader definitions are:
Gen fic: story that does not focus on romantic relationship or attraction
Het fic: story that primarily focuses on heterosexual relationship or attraction
Slash fic: story that primarily focuses on homosexual relationship or attraction
Now, what do you call a story that develops a main heterosexual pairing, a homosexual pairing and platonic relationships? GenHetSlash? (Or maybe you'd call it BtVS seasons 4 through 7. Season 1-3 being GenHet because Willow didn't realize she was gay yet.)
Or what do you call a story that is about a single character's journey which is developed through platonic, romantic and professional relationships?
The platonic and professional relationships = Gen. But as soon as a romantic relationship receives attention, it's Het. Doesn't that seem a bit odd? That Gen is defined by the absence of Het?
I rather think of Gen as the name implies. General, covering all areas and broader in scope, while Het is a sub unit of Gen, specific to romantic relationships. Gen is the larger field of play, Het is the tinier corner that only pays attention to romantic relationships.
So then, what do these labels all mean to you?
For me, I'm left with only the certainty that I like BtVS because it defies easy labels and that I really don't like labels. And this interest has mostly sprung up because I've been getting outside feedback calling "Thought You Should Know" both Gen and Het fic. I'd never bothered trying to define it as either until now and I'm still confused.