@Mozzo: the OP wasn't asking about 'an other'. That could be another topic.
'Another' is a determiner (some classify determiners as adjectives), or a pronoun.
'An other' is a determiner followed by an adjective that modifies the noun that follows it, or it is a determiner followed by a pronoun.
In either case, they mean
exactly the same thing.
Check the dictionary meanings of 'another' and you'll see that one of the meanings - "different, distinct" - applies directly to your examples. You'll find the same meanings given to 'other'.
'Another' means 'additional' as well as 'different'. So does 'other'.
'An other' became 'another' in the 13th century.
'An other' does exist, and has its place in English, but let's stick to the topic.
