I've looked into some papers about life happiness , and how work hapiness and familly hapiness can affect it.
A quick google search lead me to 2 articles :
Work, family, and happiness
Job Satisfaction and Family Happiness:
The Part-time Work Puzzle
I don't have the time to read them all , but from what I saw "work hapiness" and "family hapiness" are both parts of "life hapiness" but it seems like you could include as much hapiness sources as you want like "sport hapiness" , etc... (the last part is a personnal thought)
One important point seems to be that they're both different for men and women and are not exclusives.
For more details I'll invite you to reader the papers I linked you.
From what I've read I can tell that :
Do we really have two different types of happiness?
No , we don't. Hapiness is hapiness as a whole , but it comes piece by piece from everything you enjoy in your life.
Are the two happiness qualitatively different from each other? Hapiness is formed from everything you enjoy in your life , so the quality of everything forming your hapiness is realy personnal. Though , the studies points that men and women react differently to the work/familly hapiness balance but here again everyone builds his hapiness his own way.
Is one of them much more superior than the other type ? One could argue that familly , having kids , etc is the beautifulest thing in life , and so the best source of hapiness but as I said , it's a realy personal thing and I have no trouble imagining housewifes can be as happy as women working a lot and loving their work.