Gender dysphoria means the physical gender does not match the brain gender
Genderqueer is an umbrella term that refers to people who are not one gender or the other. They are generally specific on details of why they are not male and why they are not female.
Androgyny or being an androgyne refers to people who are a bit of both genders and feel one gender or the other does not properly describe their level of inbetweeness.
Transsexuals change genders from what they were born as.
Intersex people are born with genitals that are not clearly male or female or they have hormone conditions that change their bodies at puberty to be inconsistant to their genitals.
There are hundreds of more terms of interest but these five can be used to catagorize most people.
Personally, I was born a male physically and never changed. I never felt a need to be female in any way. Even though I feel I have a femine brain, I do not see it as a mix of the two genders or a lack of determining which one. This means I am not any of the above catagories except "Gender dysphoria" and specifically a very female brain in a very male body and always been that way. There is a very detailed gender test by the BBC that I have taken in the past and took again tonight. For elements of gender that rely on conditions of the embrio development, I seem to be female but if it relies on testosterone levels after being born, I score very male. My overall score matched males but for some aspects involving attitude, values, and compassion; I scored very female. I feel a bit uncomfortable wearing the term "androgyne" because I don't see myself as both genders but squarely one or the other... just not matching between brain and body. That being said, I do fancy the thought of being female characters in fiction (voice in radio plays, animating female characters, writing stories from a female character's perspective) and really got a thrill when wearing a mascot suit and people thought I was a female based on my actions.
The BBC test mentioned above: