While you're explanation is sufficient for the literal and minimum explanation, i think the confusion is rooted in the similarities if the two in English. I found this online and makes sense:
The words another and different are very similar in meaning and they can often be used interchangeably. ... Another difference is that the word different can be used with a plural noun. The word another cannot be used with a plural noun: These are different times.
I see that "dalsi" means another/next However when I answered it as "another woman" for "dalsi zena" , it shows as wrong. How come it is wrong?
As you can see above, "another woman" is the official translation here.
If you did indeed answer that, it may be the Duolingo grading bug. Please use "My answer should be accepted".