G: Yes. I checked legal dictionaries, Cornell’s Legal Information Institute, and actual federal cases because there is a wrinkle here—but your basic suspicion is substantially correct: there is no stable, general technical distinction in modern American law between “illegal” and “unlawful.” Most of the time they are synonyms. The rhetorical difference is considerably more reliable than the legal one.

Cornell’s Wex is unusually straightforward. It defines illegal as conduct “against or not authorized by the law” and explicitly gives unlawful as a synonym. Its unlawful entry likewise calls it a general description of conduct that is “illegal or not authorized by law.” citeturn0search11turn0search3

And courts actually encounter this problem. In United States v. Orellana, the Fifth Circuit looked at the statutory phrase “illegally or unlawfully in the United States.” Black’s defined illegal as essentially “forbidden by law; unlawful” and unlawful as “not authorized by law; illegal.” The court consequently treated the phrase as referring to presence that was forbidden or unauthorized by law, rather than discovering two neat categories corresponding to the two words. citeturn0search37

There is, however, an old distinction lurking underneath the modern usage. The 1910 Black's Law Dictionary said, roughly, that illegal meant positively forbidden by law, whereas unlawful could encompass something the legal system would not recognize or enforce even though no positive prohibition said “you may not do this.” The classic territory was contracts contrary to public policy: the agreement might not itself constitute a prohibited act, but the courts wouldn't enforce it. citeturn0search2

That distinction has largely deteriorated. Bryan Garner—lawyer, lexicographer, and longtime editor of Black's—has described the words as “fundamentally synonymous,” and modern Black's definitions essentially point back at one another. citeturn0search1

There is nevertheless a weak modern tendency worth preserving:

illegal → sounds more like the law affirmatively prohibits this act, particularly criminal prohibition.

unlawful → can comfortably mean the broader this is not authorized/permitted by law, including civil, administrative, regulatory, or otherwise legally invalid conduct.

But that is a tendency, not a rule. Cornell specifically warns that unlawful sometimes gets used narrowly for criminal conduct and sometimes for statutory violations, which is basically an admission that you cannot safely infer the legal category from the adjective. citeturn0search3 A recent Tenth Circuit decision does provide an example of the broader usage, describing “unlawful” as reaching noncriminal violations as well. citeturn0search6

And that gets to the rhetorical feedback loop you suspected

There really can be one.

Because illegal has accumulated a stronger everyday association with crime/criminality, writers sometimes deliberately substitute unlawful when they want to describe the legal condition without importing the implication criminal. Conversely, someone wanting to emphasize wrongdoing may prefer illegal precisely because it sounds stronger.

Immigration discourse is an especially conspicuous example because the legal vocabulary itself isn't nearly as tidy as the political vocabulary makes it sound. Congress has even enacted language containing both words simultaneously—“illegally or unlawfully in the United States”—despite courts finding definitions in which the two effectively define one another. citeturn0search8

So I would separate three things:

Level	Illegal vs. unlawful
Ordinary dictionary meaning	Essentially synonymous
General modern U.S. legal meaning	Essentially synonymous; context/statute controls
Connotation / rhetorical use	Illegal tends to sound more criminal and condemnatory; unlawful tends to sound more technical, procedural, or authorization-based

The important qualification is that particular statutes can assign significance to particular wording. Once you're interpreting a specific statute, regulation, contract, or established term such as “unlawful detainer” or “unlawful presence,” you cannot casually substitute words, because the whole phrase may be a defined legal category. That's different from there being a universal jurisprudential rule that illegal ≠ unlawful.

So if what prompted this was somebody objecting to a sentence on the grounds that “No, that's merely unlawful, not illegal”, I'd be immediately suspicious unless they can point to the specific legal context that creates the distinction. There isn't a general American-law rule that gets them there.

And conversely, if someone switches illegal to unlawful because the former sounds accusatory or politically loaded, that's ordinarily a rhetorical/style choice, not a correction of legal terminology. citeturn0search3turn0search11

A useful Japanese parallel: 違法(いほう) literally means something like “contrary to law,” and it encounters much the same problem—ordinary language wants a clean category where actual law is much more dependent on which rule and what consequence.