Firstly, let's try to understand who the Pandavas and Pandyans were. From WikiPedia,
The Pandavas (Sanskrit: पाण्डव) refers to the five brothers of Yudhishthira, Bhima, Arjuna, Nakula and Sahadeva, who are the five acknowledged sons of Pandu and central to the epic of Mahabharata. The Pandavas waged a civil war against their extended family consisting of their cousins Kauravas led by Duryodhana and his brothers, as well as their preceptor and gurus Bhishma and Drona respectively. This conflict was known as the Kurukshetra War.
The word Pandava (Sanskrit: पाण्डवा) is derived from their father's name, Pandu (Sanskrit: पाण्डु). The name Pandu here seems to be related to this incident,
When Vyasa approached Ambalika, she was frightened by his scary appearance, she had become pale in disgust; hence, her son was born pale. Thus Pandu's name means pale.
There's a similar word in the ancient Maharashtri Prakrit called Pandhra (Sanskrit: पांढरा), also meaning white/pale. Hence, it's possible Pandu comes from a similar etymology.
The Pandya dynasty, also referred to as the Pandyas of Madurai, was an ancient dynasty of South India, and among the three great kingdoms of Tamilakam. The Pandyas ruled extensive territories, at times including regions of present-day South India and northern Sri Lanka through vassal states subject to Madurai.
The word pandya is thought to be derived from the ancient Tamil word "pandu" meaning "old".
Hence, even though both dynasties have the same originating name, "Pandu", it means two completely different things in both contexts. However, it doesn't mean that the two dynasties didn't have any interactions. Again, from WikiPedia,
The Pandyas were fierce warriors who took part in the Kurukshetra War as per the epic Mahabharata. A Pandya king named Darshak, is mentioned as participating in the Kurukshetra War, siding with the Pandavas. You can read more in the original article here.
I originally searched for this question to satisfy a curiosity that I myself had, and having no good answer, decided to write a blog-post for the same myself :). If you liked this post, be sure to subscribe below via email or RSS.