Ramanujaya Nama: Adiyen, what is the difference between ‘Adaikalam Nan Pugundene’ and ‘Adikizh Amarndu Pugundene’? Can it be interpreted that Perumal at Thirumalai and Kachi is the sole refuge?

These two lines denote that Emeperuman is the sole refuge and me being an utter destitute(Akinchanyan), seek His refuge alone.
Notes:
It should be understood that Namazhvar sought refuge unto Lord Thirumalaiappan (Adikizh Amarndu Pugundene) and Swami Desikan surrendered unto the Lord Devadirajan of Vezhamalai (Adaikalam Nan Pugundene).