It actually is the same structure, differentiated of course.
At first glance the placement of the urethra does seem odd. But there are some facts that clear it all up somewhat.
The urethra in both male and female runs from the bladder to a spot on the perineum. In the female the urethra exits at this point. In the male the urethra continues on from this point to the end of the penis.
The urethra does not however go through the center of the penis, it is just barely beneath the skin on the underside. In the erect penis the urethra is readily discerned just beneath the skin on the underside. So ingrained is the notion that it should be in the center that most anatomical drawings falsely depict it at the center.
If a catheter is passed through the penis to the bladder you can feel the catheter just beneath the skin from the penis all the way to the point on the perineum where it enters the body on its way to the bladder. This entry point is at the same location in males and females.
In female to male reassignment some patients opt for no bottom surgery at all. Some opt for a messy construction of a penis using tissue from the forearm. Some opt to just pass off a testosterone enlarged clitoris as a miniscule penis.
The problem of the clitoris as a penis is the urethra. I believe it is generally left in place further down on the perineum... this seems totally unsatisfactory to me.
I'm not certain if this is ever done but since the urethra does not need to go through the center of the penis but can be placed just beneath the skin on the underside (as in the male) and the urethra is close to the skin surface all the way from the perineum to the end of the penis it seems like a simple surgical procedure could patch things up nicely.
If I were to work up a procedure I would think that a small incision could be made from the end of the enlarged clitoris to a point about a centimeter down on the underside. Then a shallow incision line could be made from that point down to the urethral exit on the perineum. Passing a pediatric size catheter (say about 12 Fr) through the opening at the end of the penis and then laying it into the incision and finally inserting through to the bladder should make a functioning penis with a urethral opening at the end after the incision line was closed over the catheter and healing takes place.
The tricky part would be not damaging the nerves going to the sensitive tissue at the end of the enlarged clitoris.
One thing is certain. Male to female plumbing changes are much easier to do than the reverse.
Sorry for explaining this is such gruesome detail. I just wanted to explain that the differentiation of the male penis and enlarged female clitoris is only a matter of a urethral channel that is just barely beneath the skin and is not a major difference.