I’d say it’s an alternative to Instagram, but not Flickr. A huge distinguishing feature of Flickr is that it keeps high-quality versions of uploaded photos. Instagram and Pixelfed compress to a low quality. Pixelfed’s UI also suggests that it’s more of an Instagram replacement, i.e. more about the social media aspect than about the photos. The photos are just an excuse to do social media.

Also worth noting: it uses ActivityPub, and Mastodon users (and many other systems) can see and interact with Pixelfed users in most ways that matter.

In a lot of ways it's just a photo-optimized UI for ActivityPub. Which is generally a good thing.