I don’t know exactly which one is more official and correct?
What is main difference?
There are various master’s degrees, such as MA (Master of Arts), MSc (Master of Science), MPhil (Master of Philosophy), MTheol (Master of Theology).
“An MSc student” would only cover one of these possibilities, while “a master’s student” would cover all of them. You could say “a postgraduate student”, but this would include people studying towards doctorates.
The apostrophe in “master’s” should be retained (see https://en.oxforddictionaries.com/definition/master for examples).
“Master’s student” has some official or semi-official usage ( https://www.google.co.uk/search?q=%22master%27s+students%22+site:.ac.uk ; http://www.manchester.ac.uk/study/masters/funding/living-costs/ ).