Is the difference between ワクチン (Wikipedia article) and 予防接種 (Wikipedia article) that the former refers to the medication that is injected into you (a vaccine), whereas the latter refers to the act of injecting it into you (a vaccination)? Or are there other differences between the two, such as which context it'd be used in for example everyday versus technical?
You're on the right track.
ワクチン (transcription of German Vakzin) means vaccine, the injected microbe specimens.
予防接種 might be better translated as "preventive inoculation". 接種 alone describes the act of microbe seeding, and 予防 part is optional, just for disambiguation from other 接種, such as planting mushrooms on the bed. So strictly speaking, the most exact translation of vaccination should be ワクチン接種, but ordinary people would imagine vaccine injection simply by 接種.