The biggest difference between these two words is that “another” is always singular and does not describe anything specific. “Other” is used for plural and noncount nouns that are general. We only use “the other” to refer to specific nouns.

A simple rule to help you remember the difference between another and other is: another + singular noun other + plural noun others (a pronoun to replace other + plural noun) I need another cup. (cup is singular so we use another) I need other cups. (cups is plural so we use other) I need others. (refers to other cups)

The nouns in both sentences are not specific, just like with "another". The speaker doesn't specify which other people have problems, or what other information the book has. The rules are the same as "another" except that "other" is used before plural or uncountable nouns.

‘Another’ is used when referring to something that is different or additional to something already mentioned. On the other hand, ‘other’ is used when referring to something different or separate from the one previously mentioned.