I do not see an error here.
You have fallen into the trap of numerical accuracy near critical points...
The denominator of T[z] approaches 0 for z->1/3 so the whole expression is ComplexInfinity
So what would you expect?
T[x]-S[x] you first tray to calculate each function (numerically) and then take the difference
you will get an identical zero
try also T[1/4]-S[1/4]
trying T[0.333] etc. is calculating T[x] for a point which is near the root but with a fixed accuracy
if you calculate T[0.3333333333333333] you will get a (much) higher value since it is closer to the root
try increasing the precision (say 100 digits )
T[0.333333`100] - S[0.333333`100]
you will get a number which is quite close to zero