other / different
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other
Refers to a person or thing that is not the same as the one already mentioned or known; another, additional person or thing.
Dieser Pullover gefällt mir nicht, ich möchte einen anderen.
I don't like this sweater; I would like another one.
The word 'ander' (other/different) is declined like a normal adjective and agrees with the noun. Pay special attention to the endings after the indefinite article, e.g. 'ein anderer Weg' (another way), 'eine andere Frau' (another woman).
Ich möchte bitte ein anderes Glas, dieses ist schmutzig.
I would like a different glass, please; this one is dirty.
To express that something is 'verschieden' (different), the adverb form 'anders' (differently/different) is often used in the combination 'anders als' (different from/than). This structure is very common for emphasizing differences.
Mein Urlaub war ganz anders, als ich es mir vorgestellt hatte.
My vacation was completely different from what I had imagined.
The expression 'unter anderem' (among other things) is a fixed expression and means 'neben anderen Dingen' (among other things). It often introduces an incomplete list. In texts, the abbreviation 'u.a.' is frequently used.
Auf der Konferenz sprachen viele Experten, unter anderem eine Professorin aus Harvard.
Many experts spoke at the conference, among them a professor from Harvard.
immediate / same
'ander' and 'gleich' are often opposites. 'ander' is used when something is not the same or differs from something else. 'gleich' means that two things are identical or very similar; with people, it can also be about equal rights or equal value. There is a risk of confusion because both words are used when making comparisons. The simple guide is: 'ein anderes Buch' (a different book) is not the same book; 'das gleiche Buch' (the same book) is the same in important features or identical.
Nach dem Gespräch hat Anna eine andere Meinung.
After the conversation, Anna has a different opinion.
Im Team haben alle Mitarbeiter die gleichen Rechte.
In the team, all employees have the same rights.