In the hover hint, the first translation for "artsen" is surgeons. In American English we distinguish between a "doctor" or a general practitioner and a "surgeon" (which refers exclusively to those who operate or perform surgeries on patients). As I recall this definition doesn't necessarily exist in British English(?) A Surgeon can be a catch-all term for a doctor. Does the distinction exist in Dutch, or is "arts" just a general word for "medical professional"
de arts - doctor, physician
Hij heeft zich als arts gevestigd. - "He has opened/started a medical practice."
zijn arts raadplegen - "consult/see one's doctor"
vrouwelijke arts - "lady/woman doctor"
de dokter/dokteres - general practitioner [common], physician [formal]
Ga er eens mee naar een dokter. - "Go to/see a/the doctor about it."
voor dokter studeren - "to study medicine; to train/study to become a doctor."
de geneesheer - The physician, doctor, medical man/practitioner
- het beroep van geneesheer uitoefenen - "practise medicine; practise as a physician/doctor"
de geneeskunde - the medical science
interne/nucleaire/tropische geneeskunde - "internal/nuclear/tropical medicine"
preventieve/sociale geneeskunde - "preventive/social medicine"
reguliere geneeskunde - "conventional medicine"
alternatieve geneeskunde - "alternative medicine"
de medicus [formal] - The doctor, physician, medical student
- (aanbevolen door) de (heren) medici - "(recommended by) the medical profession"
geneeskrachtig [adjective] - therapeutic, healing, curative, medicinal
- geneeskrachtige eigenschappen hebben - "have medicinal/healing properties/qualities"
chirurgisch [adjective] - surgical, operative
- chirurgische instrumenten - "surgical instruments"
Source: Van Dale Grote Woordenboek
native speaker here, "chirurg" is a specific word for a surgeon. "dokter" and "arts" are way more general. the word "arts" sounds high class to me, while "dokter" sounds very colloquial. You could call a "chirurg" an "arts", but the other way around is not necessarily true. I don't think there is actually a real difference in meaning between "dokter" and "arts", because your "huisarts" (GP) will generally be called "dokter (last name)", but maybe linguists would disagree with me here.
I don't know where you get the idea that British people use the term surgeon as a catch all term for doctors. In England a doctor is one level of qualification while a surgeon is a higher one (in surgical fields). In general this means that a doctor might perform surgery, but a surgeon is better and probably more experienced.
Higher even than that is professor, though since it is an academic qualification you never need to have been a surgeon to be a professor.
If you've read the Resident Evil books - or seen the movies - the idea of doctors keeping virus in their labs would not be as foreign. There you have a bunch of corporate bad guys who are busy developing bioweapons and some of them have a tendency to turn humans and other living animals into zombies. (Zombies! Rennen!) (Although in real life doctors with viruses in their labs are probably more likely to be trying to identify them or develop drugs to destroy them or make them relatively harmless so that they can be used to create vaccines). I'm glad I tend not to visualize what I read very well, because otherwise I would have had far more nightmares than I have actually had. Although undoubtedly helps that most of the undead in Resident Evil are too unintelligent to be the most effective of adversaries. The equivalent of Voldemort or the Waffen SS would be far more frightening.