One has three more letters. But seriously. Is there a difference between to join and to join together? For me, conjoin occurs more rarely in speech and writing.
1. I joined the army. 2. *I conjoined the army. 3. They (i.e., the conjoined twins) were joined at the hip. 4. "For a return the astrologer erects a chart for the moment, the exact moment, a transiting planet conjoins, or returns to, its birth position."
"Conjoined twins" occur normally in nature. With medical technology being at the level it is, I suppose "joined twins" might be a possibility but one would have to wonder about the mental state of two people desiring such an operation.