Asklemmy

The grey link button takes you to the comment in the same instance as you are currently using.

The rainbow pentagon button takes you to the comment in the hosting instance (which may be the same if you're browsing a local community).

I don't know many situations where one would actually click on them—maybe the latter is useful if you're worried that federation is being slow and you're not seeing votes or replies through your local instance. But the two links can be useful to copy (by right-clicking, or long-pressing, or whatever you do to copy links in your browser/app), the former if you want to show somebody else what a comment looks like through your home instance and the latter if you want to link to a post/comment normally.

The first one opens that in your current instance, the second one opens it in its original instance, as I understand it

It opens the item (post, comment) in the instance that it was created on. For example I'm on https://sh.itjust.works so if I click on that button of your post it opens this post on https://lemmy.world, which is your instance.

Maybe you can richt click on the left one and get a link to that specific comment?

It's a permalink button. Helps for linking specific comments to friends and other places.