To me, transgender is a condition and transexual describes the results of the corrective actions, the HRT, the surgery.
Transgender is when a lot of your thought process would be more consistent with what's considered normal for the opposite sex.
Transsexual would describe a person who's done something major about changing their body to match their thought process. They've become the opposite sex.
That's how I see the meaning of those 2 words.