Popular / All identical

They are quite similar.

Every community has two options on it which controls whether it shows up in Popular and/or All. They're both on by default and there are too many communities for me to make a decision on them all so in practice what ends up happening is that setting stays as the default for 95%(?) of communities so they're eligible to appear in both feeds. On specialized instances admins might choose to make communities associated with their specialization 'Popular' and let 'All' be communities from the wider fediverse but piefed.social is a general instance so the distinction is less useful.

There is another layer though:

At https://piefed.social/user/settings/filters there is a checkbox, OFF by default, "Hide posts in low quality communities" which excludes 'low quality' communities from 'Popular' (and 'Local'). Which communities those are is determined by the instance admin and on piefed.social I've done that for all the busy meme, anime and shitpost communities. Most people probably have this off so they'll be seeing some memes and shitposts in Popular as well as All.

Personally I have the low quality filter ON so Popular and All do seem a bit different to me. I dip into All when I feel like random ragebait / funnies and use Popular the rest of the time.

Curating the communities is an ongoing job - communities change over time and new ones pop up so I haven't really had time to keep on top of it well enough to make the most of the ability to designate things as worthy of being popular vs all vs low quality. It's pretty haphazard.