Transgender people are people who have a gender identity, or gender expression, that differs from their sex assigned at birth.
As an umbrella term, transgender includes bigender, gender-fluid and other non-cis gender identities.
Many transgender people are basically binary-gendered, meaning they feel they are "male" or "female" and just want their body and lives to match that polarised gender type.
Genderqueer is a catch-all category for gender identities that are not exclusively masculine or feminine—identities which are thus outside of the gender binary.
Genderqueer people may have an overlap of gender identities, view themselves as having two or more genders, no gender, or fluctuating or fluid gender or just don't have a recognised name for their gender.