A citizen of another nation present in country without required documentation or proof of citizenship. The term has undergone various incarnations with different shades of political incorrectness. One of the most egregious examples is the term WOP. This term, while sometimes described as an anagram for 'with out papers', is probably a bastardization of the Italian word guappo, one who swaggers; ie a thug.
Undocumented alien is the term du jour used by those who wish to avoid the more specific 'illegal alien' terminology. The difference is one of semantics. Persons who are in country illegally by definition have no papers declaring their presence to be legal. To be in country illegally is to be in violation of the law.
There can be many justifications used by apologists for those persons illegally present. Reasons include economic necessity, political refuge, or simply following the path of least resistance.
For those opposed to illegal aliens they have the law on their side. Persons who are aliens are either legal or illegal, pure and simple. On the other hand, if it were my family that needed sustenance, sustenance I could acquire by breaking the law, I'd be half way toward having dinner on the table.