Mr Gandhi is a rookie compared to Mr Modi, but he has been an MP for nine years now and was recently promoted as the Congress's number 2.
The headline-making statements won the two leaders a round of applause each from their audience. But they also begged a dash to dictionary for the perplexed. For the record, the Oxford Dictionary defines a politician as "a person who is professionally involved in politics, especially as a holder of an elected office."
Since both the Congressman and the BJP stalwart answer to that description, the seeming disdain was clearly meant to be more abstract. Or nonchalant. Mr Gandhi was the more disdainful - he even attributed his being where he is to "an accident of birth or DNA."
Mr Modi's comment came five days after Mr Gandhi's and so is certainly not the original thought. Did Mr Gandhi's well-received remark at a CII meeting in Delhi last week prompt the reply in Kolkata of Mr Modi, who said today, "I am not a politician. I am an apolitical person."?
The Gujarat chief minister was being dismissive about a question on his desire to be the country's Prime Minister. The 42-year-old Rahul Gandhi had shrugged off as "irrelevant" a similar question.
There is much clamour in the respective parties of both men that they be named the prime ministerial candidate for the next general elections, which are already being anticipated by many as a Rahul Gandhi-Narendra Modi showdown. The BJP has however not announced what role Mr Modi will play in the 2014 elections. Neither has the Congress as yet declared that Mr Gandhi will be its candidate for PM.