If a girl believes she's a boy trapped in a girls body she must have some idea of what a boy is and believe that is different than she is. The same applies to a boy who believes he is a girl trapped in a boys body he must have an idea of what a girl is and believe that is different than what he is. So what are the differences between boys and girls? Jimmy Kimmel asked children that question in the video below.
Notice how when one boy pointed out differences between boys and girls Jimmy Kimmel kept answering "There are girls who do that too". There are differences boys may tend to do something more than girls but that doesn't mean girls never do those things. The only differences that are completely different are biological not behavioral.
My son's school teacher told him that people say that there are differences between boys and girls but a lot of those differences are created by society. In otherwords society expects girls to act a certain way and boys to act a certain way so they do. There are people who have tried to find out the answer to this question. Two of those people are Robert McCrae and Antonio Terracciano. They had the idea to ask find out the personality differences in different cultures. If our culture was making boys and girls behave a certain way there might be others that make them behave the opposite.
Universal features of personality traits from the observer's perspective: data from 50 cultures
Do men and women really have different personalities?