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I think the difference is whether you’re viewing lemmy.ml directly (as in, the URL in your browser starts with https://lemmy.ml/), or whether you’re viewing it through lemmy.world (or whichever site you have an account on).
I wish there was a “log in from other instance” button, but I don’t know how you’d implement that.
I expected the same and became confused trying to log in another instance.
I.w
for example, you can see other lemmy.ml community and post there by going to its @ like putting
https://lemmy.world/c/asklemmy@lemmy.mlin the address bar, lets you access asklemmy on lemmy.ml via lemmy.world, and I think you can directly post to that community without login again with that instance’s credential.