Is this informal? (울고 싶지 않아)
If this means - I don't wanna cry- then what is - I don't want to cry? Are they the same??
Yes, that is informal non-polite. The change happens in the last word: 않다. Polite way would be 않아요 and formal would be 않습니다. On top of those the word also has honorific forms for the situations when you talk about someone else but yourself. So I don't think you can compare the two languages quite like "this equals that". It's more like understading the levels of formality and politeness to determine what form fits the situation.
I've seen "쟎아" but it has always been a part of a completely different grammar.
I haven't properly studied 잖아(요)/쟎아(요) endings myself yet but if I've understood correctly they hold a similar nuance as saying "remember?" in the end of the sentence or saying "can't you see that.../don't you remember that..." in the beginning of the sentence.
These are example sentences from iTalki:
A: 박물관 가자! (hey, Let's go to museum)
B: 오늘은 일요일 이쟎아! (Today is sunday! (museum is not open today))
a: 빨리 나가자 (let's leave here quickly)
b: 야! 나 아직 먹고 있잖아 (hey! im still eating)
So this has nothing to do with the original thred/question but I still wanted to put it here to explain the difference between these grammars. ^^'
The Korean levels of formality can't really be compared with the difference between "want to" "wanna" or "going to" "gonna" or "got you" "gotcha" or "did you" and "didja". For the most part, Americans don't really vary their pronunciation depending on who they are talking to.
"잖아" is for being sassy." I suppose you could characterize it as "sassy" at times, but depending on the intonation and the situation, it could simply mean "I don't want to cry." spoken in a situation where you are very familiar with your conversation partner.
If we are going to describe "잖아" as "slurred, then we would have to also define the following English words as "slurred"-- won't, can't shouldn't, aren't, etc. It is simply a contraction. Like English, Korean has lots of contractions.
Feikkisieni rightly points out the very common way it is often used to point out the obvious (I guess that could be called sassy at times, but more often it is probably just to make a point, which is often contradicting a suggestion, but can also be a confirmation.
Why don't you go home and rest. 일해야 되잖아.
Let's order steak. 돈은 없잖아.
He helped a lot. 착하잖아
She talks way too much. 귀찮잖아
I said 쟎아 is a slur I just made up. Go to endic.naver.com and search. 쟎아 is not a really thing.... I am sure other people have written it somewhere, but it's not a word.
쟎아 Has ㅑ not ㅏ
Can't, don't, wanna, wouldya, etc are all slurred phrases.... In written form.
잖아 Is a negative but the sentence carries the opposite positive meaning, so often it is sassy. Yes, it is used for suggestions. Similar to, Should we not eat something? Will you not come?
It's using a negative statement to emphasize a stronger possitive meaning. And being sassy is the most fun thinf you can do.
And I was just mistaken/confused 'cause I've seen Koreans use 쟎아 in situations where 지+않다 doesn't make sense to me:
너는 그냥 나를 베꼈쟎아. ("You just copied me") https://hinative.com/en-US/questions/1095398
"the means of "이쟎아' is 'is' but you usally use this '이쟎아' when you have opposing views for example.. there are two guys, A and B A: hey, Let's go to museum B: Today is sunday! (museum is not open today)
A: 박물관 가자! B: 오늘은 일요일 이쟎아!" https://www.italki.com/question/69587
...used in the same way I'd assume 잖아 would be used. But like I said I haven't studied any of this yet myself and as that was all I can really give to this conversation I think it's best that I decline to study more ^^' (and maybe 지 않다 in the example situations will make more sense some day...)
From Naver, [속어] ···잖아; (문장 끝에서) 자신의 의견을 강조하거나 힘주어 말할 때 사용하는 표현. 쟎아 is not a really thing the same way "ain't" is not a real thing, but it is very common slang. The following are all from Naver--
That's because you didn't want it.
이용자 참여 그 이유는 니가 원하지 않아서 잖아.
That's what I said, wasn't it?
이용자 참여 그게 내가 말한거 잖아. 그렇지 않니?
That's the third time in the last three months.
이용자 참여 지난 세달 동안, 그게 세번째 잖아.
I'm a dentist by trade,you know.
이용자 참여 내가 직업은 치과의사 잖아.
But it's about television in a specific way.
이용자 참여 그런데 구체적으로 생각해보면 TV에 관한거 잖아.