Single moms certainly are not unusual, but the basic difference is that most SMCs identify themselves quite strongly as women who have made a decision not to wait for marriage, and who have carefully considered the social, emotional, financial, and legal issues before proceeding to become mothers on their own.
Occasionally I toss out the terms SMC or choice mom in conversation, perhaps because I hope it becomes less of an unusual idea. Sometimes I'm surprised to find that others have an intimate connection with SMCs. My friend N, for example, a 30-ish grad student and mom to a 2 year old, had an aunt who had a child through donor insemination over twenty years ago. When I brought up my own thoughts about becoming an SMC, there was nothing surprising about it to her, which was nice.
In truth, my efforts to promote awareness of SMCs have been half-hearted. Not everyone approves, of course, often blaming the moms for being selfish in bringing a child into the world without a father, going against the natural order of things, or using a child to satisfy their own emotional needs. I figure the people who are not going to approve are not going to approve, and their judgment of me doesn't really matter. However, I would hesitate to bring this up with someone unless I felt they were going to treat it with respect, empathy, and compassion. I certainly did not need a lot of negative energy and judgmental thoughts (I can manage those on my own, thank you very much) while carefully thinking through my decision and plan of action.
As for the child not having a father, I believe that my child will have a father, even if he or she does not have one at birth. I am convinced that I will meet someone who will be my husband, life partner, lover, and friend. However, I am not so sure that this will happen during my child-bearing years. I've done my share of trying to meet someone, and men on online dating sites who want to form families don't always look at women over the age of 36. I expect that being an SMC takes the pressure off of dating and relationships, and that once I have a child, I can date without the pressure of finding someone in time to have a baby. SMCs who have gotten married after having their child say that their relationships are much better at this point in their life, when the pressure from the biological clock is off.
Perhaps all it takes is someone with J-Lo's celebrity status to make the masses more aware, and perhaps less disapproving, of choice motherhood. In the movie "The Back-up Plan", J-Lo plays a young woman who goes through artifical insemination to have a baby, only to then meet the man of her dreams. (Yes, I'm sure this happens to all SMCs -- not!)