Just my 2p:
Once again, it depends on context and target readers.
As penguin suggested and hm – us and Martin--cal have confirmed, the term for lay and general medical usage is “(vaccine) side effects”.
In a similar way to "adverse drug reactions" being the technical term for side effects from medicines/drugs (technical term: medicinal products), “vaccine adverse reactions” is used by the CDC, FDA, ACIP, EMA, MHRA, WHO, UK gov etc., and inevitably gets shortened to “vaccine reactions” in reports and medical journals including the BMJ.
There needs, of course, to be a distinction between adverse reactions that are definitely associated with the vaccine and adverse events which may or may not be related. To monitor vaccine safety and report adverse events, the CDC relies on the Vaccine Adverse Event Reporting System (VAERS), a spontaneous reporting system, while the MHRA has the yellow card scheme to report suspected side effects to medicines, vaccines or medical device and diagnostic adverse incidents in coronavirus treatment:
Vaccine Adverse Event Reporting System (VAERS)
Coronavirus Yellow Card reporting site
Returning to the OP, however, as penguin pointed out in #1, the article entitled Starke Impfreaktion, starke Schutzwirkung? links directly to the original article headed No, vaccine side effects don’t tell you how well your immune system will protect you from COVID-19