What does the "T" stand for in T-duality? First of all, I am not a physicist. I'm a graduate math student and recently I came across the concept of T-duality. Actually I'm studying generalized complex geometry, which according to this paper (Generalized complex geometry and T-duality) can be used to get some nice interpretations of T-duality. 
After reading some of it, I thought the "T" stand for torus, because the the fiber are torus. But then I found another paper (Spherical T-duality) defining T-duality for $SU(2)$-bundles. At first I asked myself "Why keep calling it T-duality, if the fiber are not torus anymore?" Probably it means something else...
So, what does the "T" stand for in T-duality?
 A: The name T-duality stands for Target-space duality, Topological duality, or Toroidal duality, depending on whom you ask. See e.g. this preprint or this book.
A: T duality and S duality come from the $T$ transformation and $S$ transformation which generate the modular group $PSL(2,\mathbb{Z})$.
A: It comes from S matrix theory, long before  quarks were imagined, S,T and U characterize the type of exchange in the Feynman diagrams entering the S matrix calculation, and they are called Mandelstam variables.
  
s channel-------------------------- t channel------------------------u channel           
duality meant that the sums could be done either in S channel or T channel and the result should be the same.
There is a resurrection of the scattering matrix for strings and I guess the definition has morphed to what you find in the link you gave.
It is also used in nuclear physics, where dualities are useful.
The above is history of theory in particle physics, and it was T because it came after the S of Scattering ( like y after x).
