The joke is that NeXT acquired Apple and got paid to do it.
There’s a lot of truth to it. A huge amount of the software stack is inherited from NeXT. Steve Jobs was inherited from NeXT. Modern Apple is vastly more successful than NeXT ever was, but there’s a lot of continuity there as well.
In fairness to all concerned, the MacOS to MacOS X transition was brilliantly executed. These days we take VMs for granted, but back then it was a novel idea to run MacOS 8 as a process inside of MacOS X (the "blue box"). For most users it was seamless.
It's right there in the developer APIs. All of those NS_ prefixes in the MacOS and iOS SDKs stand for NeXTSTEP.