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While PieFed is experimenting with better interoperability with Mastodon, I think it's still more useful to think of it as serving the same purpose as Lemmy. At some point you might however stumble upon a user you want to follow, at which point you'll have the option to; similarly, you might stumble upon some comments to a discussion originating from Mastodon that would not have been visible in Lemmy. I do not, however, think it's a good platform for seeking out microblog content.
Topics are just a way to organize communities. Communities are categorized as belonging to specific topics, and looking at them allows you to browse through new content in an efficient way. You cannot, however, follow a topic in its entirety.
Feeds are user-curated groups of communities. For example, ~astronomy@piefed.social combines a number of communities relating to astronomy. Following the feed automatically subscribes you to all these communities. Some might be duplicate communities serving the same purpose, while others could be related communities such as !nasa@lemmy.world and !esa@feddit.nl. All piefed users can create feeds, and as far as I'm aware Lemmy is working on adding support for them.
Hashtags are potentially useful for organizing content in communities, but I think their main purpose is to increase visibility of content for Mastodon users.
The wider fediverse fits in rather smoothly. Peertube channels such as !ewen@makertube.net can be followed as if they were communities, the same goes for forums in nodebb. Friendica users seem to live among us without issue. Mastodon interoperability seems to be slightly more janky in my experience, but improving it seems to be one of the priorities at the moment. :)
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