I consider Emma my buddy, we spend all day every day together, so, we are buddies.
But, she is not in the same realm as my friends, for many reasons listed beautifully by others, but I'll add something.
I talk to my FRIENDS about personal problems and issues that I will not talk to Emma about. I talk to my friends about my sex life, my occasional marital struggles, money worries etc. Everyone that I know, young and old, is really discomforted when their parents discuss their own personal problems this deeply with them, which to me, illustrates another difference. I don't think children want to be considered friends by their parents, if it means leaning on their children the way they lean on their friends. I don't lean on Emma when I'm emotionally troubled, I think it would be really poor mothering to do so, for that, I go to my friends. Friends are there to be burdened on when needed, our children are not.
To me, there is a difference. Me and Emma are buddies, I am her mother, she is my daughter, we really enjoy each other's company, have lots of inside jokes and other friendly type things, but we do not lean on each other the way friends do. (maya, guess you where kinda saying this too) Emma does lean on me this way now while she is little, and our relationship is a model for her about human relationships in general can be including friendships, but once she is older, I expect that she will want to lean on her friends with things she would not want to lean on me for. Already, she is stoked when she can corner one of our family friends all to herself and have them as "her" friend, and she behaves much differently with them than with us!
Also, there is no question in my mind that family and friends are different categories of relationships. I'm basing this on the healthy, close families of multiple generations that I know (not my own). Emil and I are modelling our family on the healthy, balanced, happy families that we know, none of which are radical consensual living non coercive families, all of which are very close, loving, good people whose lifestyles and family values we have respect enough for to want to emulate as much as this works with our own personal family dynamics. And in these families we choose to model, the members do not consider their friends to be on par, or of higher value than their parents, the opposite would be true (other than a normal phase in the teenage years) I don't think being friends with children is a necessary part of having a close loving and healthy family.