Short answer: No difference.
Long answer: My German friend told me that Ich habe keine lust means I don't feel like it. Fast forward a few weeks, and I got this sentence. So it's safe to assume both are the same.
I think it's like saying "I don't feel like it" vs "I'm not in the mood for it"
There's no significant difference behind the meaning of these 2 sentences.
As I am about to reach level 11 now, I feel like doing the exercise of trying to explain the meaning of the sentence (even though I am sure that by now you could explain it to me much better).
Take the German sentence: Nein, mir (es) ist nicht danach (with an elliptical subject, of course), reorder it and consider that danach means “in connection with”, “accordingly”, or “related to”. It gives “No, it is not related to me” or “No, it does not connect with me”, which is more or less the sense of not feeling like something.
I hope I am not terribly wrong and this can help future learners.
replying to kyky, actually danach does not mean for that. Danach means after that. Es ist mir nicht danach (or mir ist nicht danach) literally means it is not after me or to me it is not afterwards. Someone above had it right, it's like English's I'm not into that, though in German the cases are different
The phrase doesn't translate literally.
Word for word to get a feel of the grammar, the sentence would probably be something like "No, to me it is not thereafter" where the "it" is implied.
But this would be one of those cases where there's no value in translating it word for word like that, so you'd be better off just learning the meaning of the phrase altogether.
I'm confused about the use of "danach" in this sentence. In other sentences in this unit, it means "then", as in "then it is simple". Here it means "in connection with", or some such.
Can somebody explain what's going on? Are these really two (possibly related) usages or the same word, or two completely different words that happen to be spelled the same?
I wrote "Nein, mir isst nicht danach." because I couldn't catch it from the normal speed correctly and the slowed down sounded like "isst", however, Duolingo did not correct me at all and it did not even mark it as a typo. I didn't report because I continued before reading this thread as I wasn't sure if it was a hearing typo or again some weird idiom DL likes to throw around, and now it's too late as I already finished with that skill.
Imagine saying "Ich fühle nicht wie es" (Literally "I don't feel like it") to a German. They would ask how it's possible to compare your sense of touch to some other object's sense of touch. "I don't feel like it" is an idiom that makes sense to us, but the words are nonsense to other languages.
That's all "mir ist nicht danach" is. It's an idiom which we don't share with German. It conveys the same idea, but the words make no sense to us.
Not too sure how long ago you've written this... but danach can be translated into 'in accordance'. So anyone reading this today (2020) you should dictionary words to see their alternate uses. This is likely not an idiom as many have suggested... it simply can be used to explain someone(thing)'s accordance.
"No, (it) is to me not in accordance"... where the es is implied seems ok.