GST is made of 3 main taxes. CGST, SGST and IGST.
CGST and SGST will be charge for intrastate supplies (within state, in your case within Tamilnadu).
IGST will be charged in case of interstate of supplies (Pondicherry).
Under GST more than place of client, place of supply matters. Even if you are paid from Pondicherry but you are providing services within Tamilnadu you have to charge CGST and SGST.
Please also read Reverse Charge under GST. On GTA RCM is applicable.