Transsexual vs. Shemale?
To the layperson - these two creatures are the same and by some definitions - that's correct.
Alas, calling most transsexual's a Shemale is considered insulting.
So what's the difference?
Before we get to that…
If you're looking for additional insights in the category, these other similar chapters in this section might be of interest:
Additional chapters Included in this specific section on this subject, include:
Variations in Transgender Expression: An Introduction
What is the Difference Between Transgender and Transsexual?
What is the Difference Between Transgender and Gay?
What is the Difference Between a Transsexual and a Shemale?
What is the Difference Between a Transvestite and a Crossdresser?
What is the Difference Between a Transsexual and a DRAG Queen?
Transsexual vs. Shemale
What is a Transsexual?
A transsexual is a transgender person - starting from either a male or female platform - that’s determined through therapy and/or their own reflection they were clearly born in the wrong body. They usually have plans to change their gender via “transition” - or have already done so. 
Translation?
If you are diagnosed "transsexual" - your transgender desire is of utmost importance to your happiness and well-being and you're intently dreaming of completely changing your gender. This desire and frustration usually starts at a very early age and is something we're born with from the start.
Additional There's a number of TS (transsexual "types" you might hear about - based around where we are in the process of changing our gender)
The two most common type of transsexuals, include:
Pre-Op Transsexual
A “pre op transsexual” is a transsexual whose usually already living full time in their new gender but who hasn’t yet had the final / bottom surgery = also known as GRS / SRS. 
Post-Op Transsexual
A Post-Op Transsexual is a transsexual whose already completed “bottom surgery” - GRS. 99.99% of the time she’s been living full-time as a woman for an extended period. Generally-speaking, post-op transsexual women are amongst the most well balanced & evolved transgender women - since they’re now past much of drama associated with being transgender. However, that’s not always the case.
What is a Shemale?
Almost every transgender gal has been called a "She-Male" at some point in her trans-female journey. For me, it most often occurred back in the days of trans night clubbing - or any other time I was around relative newcomers to transgenderism. 
However, a shemale is a distinctive member of the transgender family. I define a "she-male" as a "full time" t-girl - usually with breast augmentation - that is preoperative (still has a penis) and works in the sex industry. 
The term was created by the porn industry to market pre-op & non-op transsexuals as a new type of pornography. It’s proven very successful. 
“Tranny Porn” continues to be one of the few remaining thriving sectors in that industry. Lots of trans-women working as paid escorts also use the term to describe themselves in order to leverage interest by paid dates.
However, calling a transsexual woman a “she male” is considered a derogatory term - its akin to calling her a prostitute.
Thus, in summation:
A Transsexual is a transgender person whose driven to transform their gender to the opposite of both. This is often a long, grueling and overwhelming process. A "shemale" is a term that was created by the pornographic industry to describe those transsexual women who have not yet had final genre-reassignment-surgery (still have a penis down below). A huge sexual interest and following has been for transsexual women from shemale XXX video's - but it often causing a gross misunderstanding about transsexual love reality.
Additional Main Chapters in this Area, include:
What is Transgender?
Introduction to Transgenderism
How to respect a Transgender Person
Men Dressed as Women
Urban Dictionary: Transgender Terms
Urban Dictionary: Transgender Slangs
Transgender Labels
What do I do if I think the girl you're dating might be transgender?
My husband watches shemale porn: Is he gay?
What is Transgender?
Succinctly stated: transgender is the manifestation of a person’s need to identify with the opposite gender from which they were physically born. 
In other words?
Transgender people are compelled - usually from early age - to live and represent the gender opposite from the one they started life.
What Causes Transgenderism?
There's not enough research to definitively determine what causes our need to express an alternative gender but most present thinking reveals its instigated by varied degrees of masculinzation to the brain during our evolution in the womb.
How’s that occur?
Every mammal is first conceived female: it's the default gender. Every once and awhile the most complex organ on the body - the human brain - doesn’t successfully compete the light speed trek to its final gender. Thus, you end up with a male body being born with a female brain.
What we deal with is an inborn medical condition.
It’s real.
It’s also quite challenging.
Transgenderism Defined
“Transgenderism” is an all-encompassing term to describe all forms of alternative gender expression.
It’s used to broadly describe all forms of transgender expression or thoughts. You could liken it to the term “automobile” - when describing cars. Then, based upon the particulars of each transgender person - you could include the vehicle’s make and model.
As with cars, there’s a wide range of manifestations within the broad group, including: transsexuals, cross dressers, transvestites and fetish genderists. This wide variety is one reason society at large struggles with understanding trans-issues: there’s many variations.
Most commonly, transgender women are considered distinctive & different based upon:
Sexual orientation is about who you want to go to bed with.
Gender identity is about who you want to go to bed as.
Sound like only a subtle difference? It’s not. No gay man wants to be intimate while dressed like a woman and the majority of transgender women have no sexual interest in men. It’s estimated that over 80% of transgenders are not even bisexual - let alone homosexual. Most are completely heterosexual males - who have an alternative gender identity they feel compelled to occasionally express.
Got it? 
Politically Correct Use of Transgender Terminology
The proper terminology for various forms of transgender expression is often considered important to trans-people. Some gals consider the other labels insulting. 
For instance: if you call a transsexual woman a cross dresser, transvestite, TV or shemale? She will most likely be offended. Using improper terms can cause lots of unneeded frustration.
The simplest solution?
You can’t go wrong calling any such person “a transgender woman”.