Wittiness is a gift. Some are born with it; others grow to have it – in speeches, writings, drawings or even casual conversations. You enjoy people who are witty. The ingenuity in their messages has the power to evoke spontaneous laughter by their audience. The things they say may seem incongruous to the occasion, nonetheless, they don't quite appear irrelevant. They can be ice breakers in tense situations.
On the other hand, people who throw pot-shots OFFEND, even though their subjects may not protest. (Many are also too dignified to reciprocate!) These pot-shot throwers may or may not realise their folly. They think they are clever or witty which, in actual fact, they are not. I have come across many of these characters in life. They are not people of poor upbringing. Many are products of top business schools. Unfortunately, they don't seem to have this to know their foolishness: self-awareness.
I can go on and on to illustrate these two with examples; but to do so will mean I will lose a couple of friends. These people are intelligent, but do not possess wisdom!