There are so many different gender identities out there! I am in no way an expert, but I'll try to define as many as I can right now.

Transgender(trans): when a person's gender identity does not match the sex they were assigned at birth

Cisgender(cis): when a person's gender identity does match the sex they were assigned at birth

FtM or F2M: female to male transgender(assigned female at birth and identifies as male), trans man

MtF or M2F: male to female transgender(assigned male at birth and identifies as female), trans woman

Transmasculine: identifies with a masculine gender identity or masculinity, may be a descriptive umbrella term or used on own

Transfeminine: identifies with a feminine gender identity or femininity, may be used as a descriptive umbrella term or used on its own

Demigender(demiboy, demigirl, etc): identifies partially with a gender, but not wholly

Genderflux(boyflux, girlflux, etc): gender fluctuates between no gender and wholly a gender, can vary from gender to demigender to agender over time with the same gender

Genderfluid: gender identity fluctuates between multiple genders(may be any number of genders)

Agender: having no gender, not identifying with any gender

Bigender: identifying with 2 genders at once

Genderqueer/nonbinary: identifies as something other than male or female, may be used as an umbrella term or on own for gender

Twospirit: transgender individual, gender is related to indigenous heritage

Please comment genders you would like added or any question you have! Maybe someone out there has corrections to these!