another = an + other <= "an" means "one" so use this when talking about one thing (singular) other <= use this when talking about more than one thing (plural) - Do you want another cup of coffee? <= one more - Do you want to try other coffees? <= more than one type of coffee - I lost my phone, but I have another. <= I have one more - I lost my phone, but I have others. <= I have more than one more - Another beer, please. <= one more - This bar is busy, but there are others in the area. <= more than one

You use "other" when you're referring specifically to someone or something as opposed to another person or thing. Like "I don't want that cup, I want the other one". Maybe the first cup they offered you was dirty, so you requested one that's clean. You also use it in colloquial expressions like "The other day I went shopping." Meaning you went to the mall recently. In some cases, you use "another" when you're asking for more of something, like "Can I have another slice of cake, please?" Or you could say a second piece. There's also this expression "We'll talk about this another day." Meaning some time in the future but not right now. I'm trying to give you a good clear definition but honestly I had never thought of it before. The best advice I could give you is to pay attention to how these words are used in different contexts. Even if you don't get it right you ll still be understood