You can say either one, but they have different effects.
"She is not a student" is a simple statement of fact.
"She is no student" is usually an emphatic statement, which only really makes sense when you're denying somebody else's implication that she's a student.
For example, if one professor says, "A student asked me a question about [some crackpot theory] after yesterday's lecture," another professor might say, "She's no student!
She's just some woman who slips into lectures so she can ask her crazy questions."
You could also use it figuratively, to mean that she's such a bad student that she doesn't deserve the name: "Mary?
Ha!
She's no student.
I mean, she pays her fees and comes to lectures but have you ever seen her actually study anything?
I haven't!"
ell.stackexchange.com/users/4468/David Richerby
You can say "She is no student."
This "style" is usually used for emphasis.
She is no student!
She's an imposter, just a journalist trying to get her story!"
You cannot say "She is not student".
Here you need an article.
Your edit makes your example correct.
She is not a student.
ell.stackexchange.com/users/2704/James Webster
The first sentence can mean that she is not a student despite seeming like one.
Or that she did a bad job at being a student.
This is a bit of a strong statement.
The second sentence is not grammatical.
It should be
She is not a student.
The meaning of this sentence is self-explanatory.
To sum up, the two sentences do not mean identical things.
ell.stackexchange.com/users/25052/Nihilist_Frost
The two statements have very different connotations.
"She is not a student" simply means what it says: "she is not a student, she is employed as a cleaner".
While "She is no student" probably means something like "She might be registered as a student, but she's making no effort to study"
ell.stackexchange.com/users/9574/Michael Kay
I am an educated native speaker of American English.
In both British English and American English, I believe, "She is no student" is usually a flippant judgment, while "She is not a student" does not imply any moral judgment, unless the judgment is implied by tone of voice.
ell.stackexchange.com/users/25621/John Hickey
"She is not a student" is just a statement, stating that she is not a student at all.
"She is no student" can mean different things, and is more empathic .
"She is no student" can mean that she does not study at all, she does not participate in projects, or even she does not even go to the school.
It can generally mean "She does not act like a student" or "She is not a student".
Examples: She
neither studies nor she does her homework.
She is no student!
or She hasn't ever written an essay, so she is no student.
But you can't say:
She hasn't ever written an essay, so she is not a student.
ell.stackexchange.com/users/10658/EKons
I'm always confused with that issue. Should I say    She is  no  student   or    She is  not  a student   Or are  both of them  equal? If they are, what is the difference between them?
Should I say: She is 'no' student or She is 'not' a student?
ell.stackexchange.com
<word-choice><negation>
ell.stackexchange.com/questions/71270
ell.stackexchange.com/users/12430/Judicious Allure
The two sentences  do not  mean the same thing. "She is not a student" is a simple statement of fact.  However, "She is no student" would imply that although she may well be a student, she's making no effort to study, for example.   The two sentences have different connotations. 'She is not a student' is a factual statement, 'she is no student' is a flippant value judgement.
The two sentences have different connotations. She is not a student' is a factual statement. She is no student' is an emphatic flippant judgement.