This is an image produced for a book I edited, on children born with sex development different from the typical male or female. (My talented artist-brother did it for me. He’s so talented he can even make boring line drawings on request.)
This image shows some of the kinds of variations you can find in genital development, from the typical male (figure 1) to the typical female (figure 6). The reason you can get the in-between types (some of which are shown in figures 2-5) is that males and females begin in the womb by developing the same basic sex organs, and then sex organ development diverges. (See an illustration of that by clicking here.) Sometimes the sex organs develop sort of in-between the male-typical and the female typical. (That’s why these types have sometimes been called “intersex.”)
Note that you cannot be born “with both sets of genitals.” I forbid it! No, seriously, you can’t. It’s just not possible. Read about that here.
To see the steps in male-typical and female-typical development, go here.