Not sure about the EU, but in the US:
'A Prescription,' or 'Rx,' can mean several things:
--A doctor prescribes medicine for a patient. The piece of paper or record of this is called a prescription (a legal document that informs a pharmacy that a doctor has ordered/permitted the use of the medication.)
"The doctor gave me a prescription for X.' I took my prescription to the pharmacy, and the pharmacist gave me the prescribed medication.'
--A 'prescription' can also generally mean a medicine that requires doctors authorization. Compared to over-the-counter (OTC), which can be purchased at a store without any doctor's authorization.
For a given active pharmaceutical agent (API), there may be countless 'dosage forms,' such as different strengths, instant release, extended release, liquid gels, etc, etc. You would have a prescription for a specific dosage form, i.e. 50 MG of an instant release medicine 'X.'
'Instructions,' I would understand simply to mean how the medicine is taken, i.e. take one tablet in the morning with food, take three times a day, take one tablet before bed, etc.