I have a Zoom G2.1Nu pedal. Adjusting delay settings, I noticed that I can set it according to time (as in numbers) or note duration (quarter note, dotted eight note, etc.). This part I don't get. Are the 'note duration' settings fixed at a certain BPM? And why add these settings when they're at a fixed tempo? Or are these settings derived from other delay pedals?

I hope you get what I'm rambling about.
They're a separate thing. The quarter note is a standard delay, and if it were just that setting, you'd be right - no real benefit. But when they give you a quarter and a half note, you can set a tempo via tap (or another method) and get delays to every beat or every other beat with the quarter and half note delays. That's not terribly interesting or useful, but it introduces the idea behind the interesting stuff: you can leave the "time" setting the same, and get different and increasingly exotic delay patterns without having to tap a complicated pattern or trying to sync precisely with the time knob.

The real benefits are on the triplets and the dotted quarter/eighth notes. Try them out - you'll see why you don't get those subdivisions from a standard delay pattern. They let you set a tap tempo, then they subdivide for you to get those interesting, (literally) off-beat delays that would be really hard to tap out on the fly. Again, try tapping out a dotted-eighth delay. You can probably do it after a few tries, but you wouldn't want to do it in the middle of a gig. Trying to sync to dotted eighths with just the time knob is just pointlessly frustrating if there's no milliseconds readout, and requires some math if there is - again, not impossible but far easier if you can just hit a button and let a computer do it for you.

So yes, you could physically get a triplet or a dotted quarter delay out of any old delay pedal, but it's quite difficult to nail the timing. To make it quick and easy, they give you those options so that you can tap out a precise tempo and experiment with different subdivisions by changing the note setting on the pedal, instead of sitting down and trying to do the math
Ah, I see it now! Thanks a lot for the clear answer. I guess I haven't been messing around with my pedal enough. I thought the 'note duration' delays were set at a certain tempo that couldn't be changed, because when I tried to tap out a beat while on the delay setting screen, having it set to dotted quarter note, it would then be set to the beat in a 'time' setting. Turns out, I have to exit the delay setting screen first, then tap out the beat with the delay being set to dotted eight note. And there, as you said: a dotted eight note delay at the specified tempo.

For as long as I have been using this pedal I've only relied on time settings - as you can probably imagine, it's been a struggle to set the delay and have it at a tempo that matches the song. This is very enlightening. Thanks!
I have a G2NU, how do I get to the note duration setting sin the delays? I only see times, and I can tap the tempo with an external foot switch but I want to be able to use dotted eight note, etc...
Dotted eight notes are popular for stuff like U2. It makes it so you can just tap the qtr note temp instead of trying to tap the dotted eight timing.
I know what they are for, just trying to be able to do it with the G2NU. The manual doesn't tell you but I figured it out. If you crank the knob all the way clockwise, when it reaches the maximum number of milliseconds, it changes to notes. This thing can do everything from 1/32nd note to 16 beats. I also had to change the footswitch parameters in the global settings so that it changes the bpm rather than the actual delay time when you set the tap tempo... super cool