Another, other, and different all relate to the idea of something being not the same, but they follow different grammar rules and carry slightly different meanings. The choice depends on whether the noun is singular or plural, countable or uncountable, and what meaning you want to convey.
Grammar Review: Another, Other & DifferentANOTHER
Use another with singular countable nouns. It means "one more" or "a different one": Can I have another coffee? / Let’s try another approach.
OTHER
Use other with plural countable nouns or uncountable nouns. It means "additional" or "the remaining ones": I have other plans. / There are other ways to solve this. The others (with the) refers to the remaining items or people in a specific group.
DIFFERENT
Use different when you want to emphasize that something is unlike something else in nature or quality — not just "one more" or "additional": That’s a completely different problem. / She has a different personality from her sister.
Key distinction:Another and other are primarily about quantity or choice; different is about quality or contrast.