The short answer is “no”.
There are cultural differences, and differences of size of the larynx and vocal folds, but functionally all voices have the same scientific registers available to them – fry/Mode 0, chest/Mode 1, head/Mode 2, and whistle/mode 3. All voices need to be trained to use their full pitch potential in chest and head registers for optimum function and health, regardless of the styles they sing in. All other things being equal, larger larynxes will have an easier time singing lower pitches than smaller ones.
All the same structures are present in males, females, and intersexed people. What is different is size and shape. Before puberty all voices are more alike, but the male’s hormones cause the larynx to become larger and the folds to lengthen and thicken. Bigger instruments produce lower pitches more easily. This is why the voice’s comfortable pitch range drops at puberty in most men.
If a woman’s body has enough testosterone, her larynx will go through the same transition, even though anatomically she is a woman. Once a larynx has grown, it will not shrink again, so the tendency is for the comfortable pitch range to drop as the instrument grows and/or the folds lengthen and/or thicken.
If a person born as a male transitions to female, the larynx cannot become smaller, but that person can learn to speak on higher pitches if they wish to approximate the cultural norm. Large larynxes speaking and singing high pitches have a different timbre than small ones on the same pitches.
There are physically normal males who have small larynxes and normal women who have large ones. Sometimes it is hard to tell by phonation alone which gender one is hearing when they speak or sing. However, there are speech patterns that are typically different between men and women that are also a factor, and two people talking at the same pitch using typical gender-identified mannerisms and vocabulary can sound like “one or the other” without too much confusion.
Culturally, low-voiced women used to be encouraged to speak in higher ranges than today. Listening to radio shows or films from the 1930s and 1940s provides much evidence of that. Now, many young women aim their voice so low that a lot of “vocal fry” creeps in. Men can fry too, but it is much less common.
Similarly, after puberty many boys artificially restrict the pitch range of their speaking voices to low pitches to project a mature, masculine identity. However, much of the popular song repertoire requires very high singing.
It is a complex interaction of biology and culture that creates what we perceive as female and male voices.