@popolon @Hyolobrika @thor
It's not same writing system, while both do evolved from the Brahmi script (Influence of the Brahmi script goes till the Japanese Kana writing system) but in the time they have diverged alot.
North India uses the Devnagari script and it's variant while the South uses Tamil-Brahmi and it's variants.
By the way, many linguists speculate that the Dravidian language family are related to the Uralic family (Hungarian, Finnish, etc)