What is the exact difference between a mezzo soprano and a soprano? Have heard that both have almost the same range but what is the exact difference? If mezzo is slightly weak in singing in head voice, then what can she do to improve the same ?
Technically speaking, a mezzo soprano tends to favor the lower and/or be overall better suited towards the lower soprano range (though not an alto) while still having a soprano timbre overall, though usually a bit darker as a result.
Ideally, a mezzo soprano is a mezzo soprano and it thus not 'slightly weak' (as you put it) compared to a regular soprano -- ie, this is their natural voice which just happens to be lower than the average soprano, and their is nothing wrong with this. Their voice should be further trained in it's natural tendencies for best results, not pushed towards something it is not.
This is of course assuming that they are receiving proper instruction and practicing with good technique to be considered a mezzo soprano.