other +singular or plural it means the remaining one or ones i need the other car. my other books are on the shelf. it can mean additional: i have no other friends only sarah. you'll solve this problem, one way or the other you have no other choices. another+singular, it means a different one or additional this pencil is broken i want another one. i need another cup of tea, please i need another chance. for more information, check: www.yhefreedictionary.com

Both can be adjectives or pronouns: Another = one more in addition to (or instead of) the one I already mentioned: I have a book, but I need another / another book. One student left his raincoat in the class. Another student left his hat. (= in addition) I have a pen but it's broken. I need another (another pen / another one) (= instead of) Other = more than one more of X in addition to (or instead of) the one(s) I already talked about. Some of the students want the test on Monday; other students want it on Wednesday. None of these solutions are good. We need other solutions (others).

as far as i understand that other meaning 'different' like "the other way " another would mean that you add something more "another friend came" hope this helps ^^