"This is Hip Hop and them nikkas should know what time it is"
Pretty much sums up what Nas and Jay thought of each other at a certain period. Nas has said during the beef that he always looked at Jay as Biggie's little homie and when Biggie died and Jay tried to claim king he slept on him. But there was always a level of competition. From Jay's standpoint, he was a fan of Nas, just like most New York MC's were at the time period, as a "rappers rapper". He felt slighted by Nas not showing up to the Reasonable Doubt sessions or the Dead Presidents video, but Nas was particularly aloof during those times, if you weren't from QB and you weren't Wu-Tang then Nas didn't really fukk with you.
A misconception if the beef is that Jay went after Carmen specifically because he was obsessed with Nas, this is false. He pursued Carmen BEFORE he knew she was Nas's woman (according to her) and after he found out, he simply didn't care. He was still a fan of Nas and used to ask her "weird" questions but he didn't get with her with the objective of using her against Nas, they had an on-off again affair that lasted several years until "Is That Yo Chick" dropped.
As for them being friends now. They put all the beef and bullshyt behind them and like grown ass men decided that they were better as allies than enemies. You could tell both of them had become tired of the battle being such a big portion of their post 2000 careers. Plus their both the two last MC's standing amongst the mainstream from that 93-97 golden age of Hip Hop. Their the only two who can stand in a room and look at each other and see someone who went through 3-4 generations of the genre and remained relevant, you HAVE to respect that about each other. Before Drake, J.Cole, Kendrick, Krit, Luda, Game, Jay Electronica, Cam'ron, Lil Wayne, 50, Ja Rule, DMX, Eminem, etc. There was Illmatic and Reasonable Doubt.