Transsexual just means you’ve had some kind of trans related medical intervention (usually bottom surgery, but it can sometimes be used more broadly too).

Not even that is something that's universally agreed upon.

For example, from Whipping Girl:

It is common for people to assume that being or becoming a transsexual involves some kind of “sex change operation.” However, this is not necessarily the case. While some transsexuals undergo numerous medical procedures as part of their physical transitions, others either cannot afford or choose not to undergo such procedures. Indeed, attempts to limit the word “transsexual” to only those who physically transition is not only classist (because of the affordability issue), but objectifying, as it reduces all trans people to the medical procedures that have been carried out on their bodies. For these reasons, I will use the word transsexual to describe anyone who is currently, or is working toward, living as a member of the sex other than the one they were assigned at birth, regardless of what procedures they may have had. Further, because there are so many different paths that a transsexual person may take toward living in their identified sex, I will use the word transition to describe the process of changing one’s lived sex, rather than in reference to any specific medical procedure.

Would be cool if we could have consistent definitions for words, but doesn't seem like that's likely to happen.