The term “illegal alien” or “illegal immigrant” had been used to describe those who came to the US without permission and proceeded to establish residence without authorization. Since around 2000, however, many news sources at the behest of immigrant activists changed their terminology to “undocumented immigrant” instead.
Not only is the new term less accurate than the old one, but it also confuses the reader because the word “undocumented” can have two meanings. It can refer to those who never had proper documentation and those who don’t have the required documentation on their person right at that moment. It is kind of like when you are stopped for driving without a license. You may have it at home, just not with you in the car.
The term “illegal” means that your continued situation is not legal and thus you are an “outlaw” in the Old West sense of that word by being outside of the law until you are apprehended and dealt with by the legal system, in this case, US Immigration and Customs Enforcement (ICE). Almost always, illegal immigrants knew they were breaking American law by not going through proper channels to immigrate here legally.
Moreover, since they did not come to the US legally, they still retain their citizenship/immigrant status of the country they left, which is properly referred to as “alien” status. Therefore, the term “illegal alien” is appropriate and more meaningfully descriptive than the politically correct term “undocumented immigrant”.