Difference between 'during' and 'while'?

[snowy]

English Grammar Tests, Elementary Level

ESL/EFL Test #94 "While, during and for", question 9

......... my stay in hospital, the nurses looked after me very well.

(a) While
(b) During
(c) For

English Grammar Tests, Elementary Level

ESL/EFL Test #94 "While, during and for", answer 9

During my stay in hospital, the nurses looked after me very well.

Correct answer: (b) During

Your answer was: incorrect
While my stay in hospital, the nurses looked after me very well.
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why use "while" is wrong? please explain.
thanks
snowy

[Torsten]

'While' is followed by a clause or a participial phrase.
'During' is followed by noun.
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