We Never Know
No Slack
If someone is on my land without permission, they are illegally there.Trespass refers to personally or organisationally-owned land and property, not a country, which have specific laws and statutes including the ability to legally declare asylum. Even so, you wouldn't call someone who trespasses on your private land "an illegal". That is language reserved exclusively for people who enter, or stay in, a country illegally, because it is specifically designed to diminish their humanity. I think that's the point being made.
If someone is in the US without going through the legal process, they are illegally here.