Vocabulary: ‘another’ and ‘different’ 
Pre-intermediate to intermediate level (A2-B1)

Would you like another drink or something different? This is asking if you want one more beer or a different kind of drink, for example, a lemonade.

To start, here’s a dialogue between a language student and their (his or her) host.

Host: Frank, dinner’s ready.
Student: Just coming. What are we having today?
Host: Lamb and potatoes. I’ve cooked some mashed potato, some roast potatoes and some boiled potatoes.
Student: Great. Any other vegetables?
Host: No, just potatoes.

15 minutes later …

Host: Would you like another potato?
Students: Thanks but I’m full.
Host: Oh, I thought you liked potatoes.
Student: I do but is it possible to have some different vegetables too? We’ve had potatoes every day for a week.
Host: I thought you wanted a cultural experience!

(Don’t worry, the dialogue is not meant to be serious)

If you want more of something, you can say:

‘Can I have another piece of cake?’ or ‘Can I have some more cake?’ but you shouldn’t say ‘Can I have a different piece of cake?’

However, if you want more choice, you can say, ‘Do you have any other sandwiches’ or ‘Do you have any different sandwiches?’. With this meaning, ‘other’ and ‘different’ are very similar. Sometimes ‘different’ is possibly a little stronger and can show you want something that is different in more ways. For example

‘Do you have any other sandwiches?’
‘Yes, we have cheese, bacon and salmon’

‘Do you have any different sandwiches?’
‘Yes, we have baguettes, pittas, ciabattas. You can have cheese, bacon or salmon in all of them’