I did a lot of research on this
While it is possible to be what most people think of when someone says intersex (both organs) it is much more common that a mistake in the genetic code of a person causes traits of both sexes to appear, meaning some lines of code have female traits and others have male traits. For example, a person who appears female could have masculine body hair and a masculine voice, or there could be genitals from both sides, such as male anatomy but with interior female anatomy rather than a scrotum, female anatomy with undescended testes, small exterior male anatomy (not all who fit this condition are intersex), large female exterior anatomy (not all who fit this condition are intersex), or the genitalia of one sex and the characteristics of another (male anatomy with female-appearing body hair and a female sounding voice or female anatomy with male-appearing body hair and a male sounding voice).
Intersex people can identify as whatever gender they want but most anatomically lean towards characteristics of one gender and are assigned that at birth. However, some parents cruelly decide to have surgery performed on their child to make them fit one gender more. This is not okay. The child is the one who gets to decide what is done with their body when they are old enough and ready to make that decision.
There are even places that perform these surgeries without asking parents or even telling parents.