Transsexualism or Transsexuality is a part of Transgender .  The actual definition of it is debated, some people say it only refers to transgender people within the Gender Binary, others say that it only includes those who actually want to transition

The most known 'kinds' of transsexuals are male-to-females (MtFs or Transwomen) and females-to-males (FtM or Transmen).   However, tN (-to-Neutrois) and others are starting to crop up as people are becoming more accepting of Non-binary genders and that people can feel the need to change their body to fit those identities.