There's a lot of continuity, and it's just semantics, but the neoconservatism of the '90s was a successor to the Reagan Doctrine that sought to maintain "benevolent global hegemony" with what Bill Kristol and Robert Kagan referred to as "a Neo-Reaganite foreign policy of military strength and moral clarity". Reagan was reacting to a policy of Détente widely believed to have failed after the Soviet invasion of Afghanistan while the neocons saw themselves as proactive in their opposition to Clinton era reductions in military spending, conversely seen by the public as common sense with the Soviet Union gone. They were pretty pessimistic about building off their idol's success because it seemed like nothing could galvanize a country divided by hot-button '90s Culture War issues, save for what a 2000 defense review described as a "catastrophic and catalyzing event- like a new Pearl Harbor".
Yet at the same time, Reagan's actual approach in action was hardly what I would term to be "neoconservative", though obviously every neoconservative would attach themselves to Reagan's legacy as part of what prior to Trump anyway, was a broad based latching onto Reagan's legacy to legitimize various positions that in a number of cases went beyond what Reagan would have deemed acceptable. Hence the old line that "Reagan couldn't survive a primary today".
The neocons were certainly part of this "True conservative" dynamic and milked it for all it was worth until they ended up on the outs themselves.
They say the revolution eats its own.