An undocumented migrant is a migrant without current proper documentation.
Just as a driver without current proper insurance is an uninsured driver.
Migrating without documentation and driving without insurance are both currently illegal. The concept of people breaking the law in either way is unpalatable though we know it happens for a wide range of reasons and both are being dealt with by authorities who make and enforce the law. I have never heard of someone driving without insurance, or even someone with insurance but speeding, referred to and reduced to being an "illegal driver", why should migrants - some of whom do so in desperate attempt to save their lives and only need nudging down the asylum route or have been trafficked here - be dehumanized and reduced in such a fashion that we do not do to uninsured drivers who, just the same, lack proper documentation. Yes, some come and take the piss - but a lot of those are holiday-cash-in-hands from the States, Canada, and so on but they tend to be labeled as "overstayers" by the media, hence why some think that undocumented migrants can't be White. Which is a laugh - the main undocumented in the Australia are White Brits who overstay, few complaints about them in our media. And the reason it's mostly them is because they're less likely to have their documentation checked as closely as people from other groups and countries.
All that separates the people you support and the people you have contempt for is documentation and leaving that out negates the ability to properly discuss the massive issues around documentations. Because the whole system around documentation is a real money maker for the government and with all the ideological babble about letting good migrants in, it's far more about keeping immigration profitable for them (hence why the price to do so goes up well above inflation every year and people need more than ever to get to Permanent Resident).
I am a documented migrant, have lived in the UK for ten years. I hope my children will defend me and other migrants in the future as the man in the article has done. Mainly as I, as a documented migrant, get intimidated and abused by people regularly. I've had people try to call false allegations on me because of stunts like this. It hurts people. Britain's going down the road of America, where any immigrant and even native borns that have "the look" will be pulled into the police stations to prove documentation and have their homes trashed on an almost weekly basis because of stunts like which get a lot of malicious fake calls. I have kin who have had this done to them in the States, and they're Native Americans, that's bitter, but that's what happen when this rhetoric becomes normal. The rhetoric needs to be challenged - the government is already dealing undocumented migrants well and treating them as sub-humans like this campaign does do anything to help, it harms people.