Could you explain the difference here? If he is undocumented and cannot legally purchase a firearm would it not satisfy both phrasings or does the latter (illegal firearm) refer to weapons banned from anyone possessing under law?
Typically saying "illegal firearm" means it is illegal for anyone to own the firearm in question regardless of the person's status or how they got it. If a person is barred by law from possessing a firearm then it is possible for them to have a "legal firearm" in their possession; for example, if someone not barred by law owned the exact same firearm then there would be no issue.
But I read the post in the manner that I'm guessing was intended, so I personally don't see it as a big deal.
The first time I read rayiner's post, I took him to mean a firearm that is illegal for anyone to purchase or own, i.e. an "illegal firearm". Reading it again, I realized his phrasing was ambiguous and he could have meant "illegal possession of a legal firearm due to immigration status", hence my edit.
So basically, it could be a legal firearm possessed illegally, or a banned firearm, based on his wording.
Edit: Thanks for the clarification below.