The left links to the post/comment on your current instance. The right links to the post/comment on the instance it was sent from. You'll see that on this comments the links do differ.
this post was submitted on 15 Jun 2023
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Adding to this - when you want to fetch content into your instance, you should search for the url that you get when you click the right button.
One links to the original instance, the other to the post/comment on your instance. If they're the same it's because the poster is from your instance.
If you're viewing a post that originated on a different server (federated post), the chain icon opens the post through the server you're on, and the colorful fediverse icon opens the post on the actual site it started on.
Try opening a post from your "All" feed and compare the links.