When to use the word "Another" and when "Other"?

Since the last thread I posted came out quite educational, I’m suggesting another discussion. What’s the difference between Another and Other. In my opinion, the word “Another” means an additional one of the same thing whereas the word “Other” means being the one distinct from those first mentioned. However, it might not always be the case. There are some examples and definitions here.
What do you think about this?

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We discussed this in several threads and have lots of exercises on this topic. Here is just one of threads:

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I didn’t check before posting, I was so hyped from the last thread and just posted.
I apologize

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