Another can, indeed, mean one more of the same thing, as in the pizza example given above. But it can be used as well to describe something a little bit different, but in the same category: " I don't like this chair, it is very uncomfortable. Do you have another one?" it is like taking "an" and "other" and making one word! "Other" by itself means something different, an alternative. " I did not like that restaurant, but I loved the other one we went to last week."