Are "write out a prescription" and "make out a prescription" used more or less interchangeably?
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Yes, they are, though "write out a prescription" is more common, as evidenced by a Google search and an Ngram graph.
Yes, although be careful - "make up a prescription" would be to supply the drugs listed on it.
Once upon a time it would be to actually make up, i.e. produce, the medicine required in the pharmacy - now of course it's just to sell the correct boxes of pills.
"Write out" carries more of a connotation of the physical act of marking a scrip sheet, whereas "make out" gestures a bit more toward the possibly metaphysical act of bestowing the prescription itself.
(I would say that's a slim enough shade of difference to be considered 'interchangeable')