The gravitational wave events that are being detected regularly now last a few seconds - they are the last few seconds of a process that took millions of years, as the two objects first orbited their center of mass from large distances, and slowly, slowly got closer together by constantly radiating very very low frequency, low amplitude gravitational waves. Finally, when they get really close and are rotating really fast, the frequency is high enough and the strength strong enough just before merging that normal GW detectors pick up the final moment.
So there are many many more systems in the early stages of GW radiation, radiating very tiny GW.
Think of it like this, there are about 7,900,000,000 living people on Earth. While only a handful are taking their dying breath at any moment, billions are breathing.
The GW events that are being detected are the occasional "dying breaths" of rotating pairs of objects, but the NANOGrav background comes from the billions still alive and rotating.
These make up the very faint GW background that NANOGrav and the other pulsar timing arrays say they have found strong evidence for. They chose the nanoHz part of the spectrum as the one they decided they could separate best from instrumental noise. The signal they have is supposed to be the sum of many, many different oscillations at the same time, all at slightly different frequencies.
Basically they have evidence for a signal at a confidence level that indicates it is likely gravitational waves -- not just noise.
So no one can not pick out one of these signals and say "there it is!". The observations were made via long term (12-15 year) monitoring of very tiny shifts in signals from 60 to 70 pulsars from widely distributed directions.
Those tiny shifts in arrival times vary a bit more than expected based on the equipment they use, so they say they've detected GW background by using very complicated statistical analysis.
I posted a question a while ago Main assumptions for ~4 sigma confidence superimposed gravitational waves from lots and lots of distant supermassive black hole pairs were detected? but a moderator told me
I'd recommend narrowing this down; there are a large number of very different assumptions and statistical methods used. An answer addressing all of them might be comparable in length to the paper itself. I'd also recommend making it clear that it hasn't been confirmed that, even if the signal is indeed a background, the background is actually from supermassive black holes; other models work fine (Check out the paper on explanations with new physics for more information.).
and I realized how complicated the whole thing was so I (at least temporarily) deleted my own question and decided to wait until I could really dig deeper.
Of course this is similar to how the Cosmic Microwave Background was first detected as well! It was simply microwave noise at a level higher than could be explained by the noise level of their equipment.
That elevated noise that others might have dismissed was the key to understanding the Big Bang. So while we can doubt that their complicated statistical analysis is conclusive, we should still take the result very seriously.