What’s the difference?
I had a scary reaction to penicillin once, though only after being on it for days...
https://www.merckmanuals.com/home/drugs/adverse-drug-reactions/allergies-to-drugs
Allergic reactions can be life-threatening. Adverse reactions tend not to be as serious (although they are often things we don’t want to experience).
Why the difference could be important? An example: One of my sons, when a baby/toddler, was given a particular antibiotic. He didn’t develop an allergy to it, rather, he had severe GI upsets to the point that we stopped giving it to him. If that had been called an “allergy” then that medication (still in use) and its close relatives would not be available to him if he needed them. Now he’s an adult, and that family of antibiotics is open to him, if he needs them.
My other son had an allergic reaction to an antibiotic. (Hives and swelling). Although that particular medication is seldom used these days, he should never take it. Would he react the same way, all these years later? It’s not worth taking a chance on.
Another example: 325 mg aspirin, chewed and swallowed, can help stop a heart attack. I’m having symptoms of a heart attack; I’ve said I’m allergic to aspirin. What kind of reaction did I have? If it causes my lips to swell and my breathing to become difficult, I’m not taking the aspirin. If it makes me feel slightly nauseated, I’m taking it right now (while I’m calling 911 and waiting for the ambulance).