First, every girl with a dick you can call a dickgirl (as the term itself describes it).
That's not necessarily true. Most of these terms/titles/etc already have some level of a base definition. It's fictional words/universes in games that make things difficult by straying away from them. So, if you were to toss real titles/views/etc into a game, your second point would look something like female/male/futanari/trans. Of course, provided Futanari existed in the real world.
Futanari (literally: dual form; 二成, 双成, literally: "[to be of] two kinds"). Literally the Japanese word for Hermaphroditism (an organism that has both kinds of reproductive organs and can produce both gametes associated with male and female sexes), or more recently titled as 'intersex' by activists. Futanari, in the fictional view, almost exclusively have sperm along with proper female bodily fluids. Whereas true intersex people will only reproduce with one way or the other, if at all. Or at least there's no reports of any one intersex person reproducing with both.
Whereas 'dickgirl' (or cuntboy, for the reverse), male-to-female (transgender/transsexual person, respectively, who has not had genital surgery. By the traditional definition of the aforementioned word, a dickgirl is simply a pejorative term for a trans person. No different than shemale or something of the variety.