Basically, one means the scientific anatomy and classification, and the other means more of a statement on the soul and personality. However, it's confusing to know which term applies to which.
With me, my thing is I care less about having a vagina and the legal classification of being a girl, and more about having at least enough physical representation facially to be able to realistically showcase the softness, kindness, and beauty that comes with being a girl, and being able to "go" with female outfits as opposed to male outfits. I honestly do not think of things in terms of gender, but more akin to what I want to express with my personality traits; I just can't by any extent express the extremely soft and cute personality I have, in a realistic no-laughs manner, with the face and features I was born with (and I do not mean anything against MTF's who don't quite pass, but trust me, so far, I'm the most masculine-looking MTF here - I look identical this and I'm only in my mid-20's:
http://i1227.photobucket.com/albums/ee437/RPlace123/ravens-portrait-deborah-allison.jpg ) and that's the face I'm hoping to medically and surgically soften, both to feel more confident in my skin, and to feel natural when I take pictures, look in the mirror, be with friends, and when I truly am myself. There's really no such thing as a "be yourself and people will see you as that" when you look as extremely androgenic as I do, the human mind just isn't able to comprehend such extremities and I've never met anyone who's ever tolerated my real personality for long without laughing or making jokes, even defreinding me all together.
I actually do not have one friend at the moment because I am indeed strong enough to still be myself; people hate the way I look and I've lost every friend I've ever had because all of them have said "I just can't put up with how you act vs. what you look like." I repeat: I do not have one single friend in my life and I am living proof that New Age Therapy Confidence crap does not work in extreme cases.
Now, who knows what I'll care about once I get all that accomplished, I have a strong feeling that once my life improves in terms of confidence, appearance, and literally a social life, that I'll probably move onto feeling that I won't be able to accomplish a romance and sex life without the proper genitalia, but for right now, I feel like my face is what defines my gender to the outside world most of all; having a different genitalia would not make me feel like a girl in the least. I mean really, what does having a vagina prove to the world? Even if you pull down your pants for every person that doubts you, it doesn't stop people from calling me ugly or crossdresser or caveman or whatever if I still do look extremely like a man. And since those particular comments are what hurt me (if someone points out that I have a penis, I give less crap), I want to tackle my facial appearance most of all. Weird situation, but I feel like it's one that reflects the times.