The T-50 is an internal company designation. It has nothing to do with function of type, ie T for Trainer.
I believe that there are some deviations but basically as detailed on Wiki
Sukhoi - Wikipedia, the free encyclopedia
'Sukhoi prototype designations are based on wing layout planform. Straight and swept wings are assigned the "S" prefix, while delta winged designs(including tailed-delta) have "T" for a designation prefix.'
For example the Su-27 was developed by Sukhoi as the T-10
Sukhoi Su-27 - Wikipedia, the free encyclopedia
The Su-47 was developed by Sukhoi as the S-32/37
Sukhoi Su-47 - Wikipedia, the free encyclopedia
The South Korean T-50
T-50 Golden Eagle - Wikipedia, the free encyclopedia
TJ