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.

Every server just has a cache … there is no profit for the whole network …

I wouldn’t say that caching is no profit. Yesterday there were several times when lemmy.ml was struggling or effectively down for some people, but despite complaints over there I could read lemmy.ml communities just fine through my instance. Caching meant that I was isolated from the service interruption, and the lemmy.ml server was isolated from my contribution to its load.

I have several, but in addition to some that others have already mentioned, these long-runners are quite good:

• Carciphona (ongoing)
• Digger (completed)
• Everblue (ongoing; might be back from hiatus?)
• Habourmaster (ongoing)