I am American, not British, but assert that scrip is more correct for shorthand version of a doctor's prescription. Importantly, the suffix is -tion, not -ion. I learned at an early age that Doctors wrote scrips and playwrights and other writers, etc. wrote and submitted scripts, or manuscripts, for review.
However, there is common usage of both.
Are there any doctors on here to weigh-in?
I've no idea about in the US, but In the UK, we talk of a doctor's prescription.

I vaguely recall once hearing someone say "script" for "prescription" but that's just an informal short-form.

In my experience, a scrip has to do with money: http://dictionary.cambridge.org/dictionary/english/scrip