Why might one doctor prescribe different medicines for two people with the same illness?

doctors prescribe different types of medicines and syrups for multiple reasons

1. for different sicknesses for example: what they give you for a cough they cant give you for a sore throat because that medicine helps a cough.

2. for different ages. Example: they wont give a young child pills because most children aren't able to swallow them so instead they would give them a syrup

3. Just easier for the person. Example: you may be a busy person that doesnt have time to measure out exactly 10ml of something and instead give you a fast working capsule instead

4. whats available to them to prescribe. Example: there may be a capsule, a tablet, and a syrup that all do the same thing and they only have the syrup, so they will prescribe the syrup because it would be pointless to prescribe something you cant get.

these are just a few i came up with, i have no experience in the medical field just common sense