Most doctor’s office personnel (including the doctors themselves) don’t distinguish between the two either - I know this from experience. After a point the intellectual laziness just gets to be tiresome and one goes with the flow so that it is at least documented in a way that something that causes life threatening reactions doesn’t get prescribed.
I also try to tell doctors about certain migraine food triggers (because many meds have some of mine in them as derivatives or additives). They chalk these up to allergies as well, even when I know better.
I must be pretty “old school” but I think the difference is pretty important. To be honest, though, sometimes trying to explain the difference is difficult and time-consuming, not to mention fighting an uphill battle. I’ve spent considerable time painstakingly explaining the difference to folks and found that the effort was to no avail.
These days, with EMR, there’s probably not really a way to differentiate in the documentation between allergy, adverse reaction, or migraine trigger, unless it’s set up so that both the “allergen” and the reaction is listed: food or medication: chocolate; reaction: migraine trigger.
If someone tells me that they had a genuine serious reaction to a medication, I do try to reinforce that they really do need to never take that medication again. I’ve also had people say “that was years ago, I don’t know if I’m still allergic” and I strongly discourage experimentation to find out. (Years ago I encountered a case of someone who did exactly that with disastrous results).