Scientists that work in drug manufacturing can have a variety of backgrounds. It also depends on what you mean by making drugs. Scientists that are trying to formulate a compound into a delivery system will probably have a PhD in pharmaceutics. Scientists working on drug discovery and design will probably have a PhD in medicinal chemistry. Scientists working on discovering how the drug actually works in the body may have a PhD in pharmacology.
Of course, these are all generalizations. I don't have any experience in industry, but maybe others that know a little more about it can chime in.
In short, Mike's right.
Generally, drug development starts with the chemists trying to develop drug libraries. Drug libraries, or groups of compounds designed around specific biological parameters (ie: ACE inhibitors, GPR30 agonists, ER-alpha antagonists) are useful means for trying to identify potential drug candidates. Often, senior scientists give can bracket specific classes of drugs that they'd like to pursue, give an idea to a chemist, and the chemists will go synthesize any thousands of compounds by tweaking specific functional groups. Naturally, there are many types of chemists, so analytical and medicinal chemistry are prized subject areas. Often obtaining a PhD, Masters, or taking specific electives can get you towards this career.
Next, any dozen of successfully synthesized compounds are "handed-off" to biologists for classification and identification. Naturally, many compounds are analyzed for given parameters. These can be as simple as determining nuclear receptor binding affinity, metabolite identification, or a drug's mechanism of action. As such, biologists usually work in tandem with chemists to determine "successful" compounds by reverse-engineering their success through the progressive modulation and tweaking of specific functional groups. This'll help the chemists build better molecules, send drug candidates off to the FDA for patent filings, and HOPEFULLY, send a drug off to phase I/II clinical trials. PhD's and BS degrees aside, there's a role for pretty much any scientific background in this field, examples include: immunologists, microbiologists, geneticists, toxicologists, and oncologists.
I realize that this was probably WAY more information than what you wanted to know, but if clinical research interests you it's probably more beneficial to go PharmD than PhD. It'll cost you more in the short-run to opt into pharm school, but if you go PharmD, you won't have to do the 2-3 post-doc experiences before getting lucky and obtaining an industry position. I work with several PharmD's that have done 1-2 research fellowships and they've specialized in drug formulation, pharmacogenomics, and toxicology. I have not had the opportunity to meet PharmD/chemistry PhD's, but that would be pretty cool.
In short: it's your choice. You can "make drugs" by getting a degree in anything. Hope this helps.
