When I select "Duplicate particle systems" a copy of the first particle system is created. This copy can be edited in Particle edit and I can even add new particles there. But if I change any settings (for example, change Children, Root, Material & etc.), then these settings also change in first particle system. How can I duplicate a particle system so that I can edit the copy, but that this doesn't affect the first particle system?
you have to play with system block and data block so you don't have the same particle system applied twice. Probably you'll need to click on that "files" icon (that let you duplicate the particle system, starting from a cloned version of the original one)
This is correct:
check how to work with different emitter settings:
this is wrong (see the number 2 that means that the particle system is used twice)
I get what they are asking cause I have the same issue. I have a animal head that I groomed. The first groom is to determine flow and is done with the first particle system. I want to add some more randomness to the hair, but keep all the groom settings I just made in the particle editor. So when I duplicate the particle system, I need to be able to duplicate the particle settings, but be able to change the child settings without changing my first particle setting. Thus, I need a duplicate of the original settings. Currently it links the original settings only.
Thankfully, someone made an addon for this that works with Blender 2.93 beta https://blenderartists.org/t/duplicate-edited-hair-particles/1247900