I know people of all sorts that have been illegal. I even know a Canadian and other Europeans that have been detained and deported, but also known 'illegal' Asians and African people. The majority though, especially in the South are going to be South American.
One minor problem with the statistic on non-Mexican people right now is that a portion of that population is due to a massive overload of the immigration system, so you can be "illegal" after your visa expires (eg. student or work) because you've done all the paperwork but the INS is currently more than 1-2 years behind on processing paperwork so your status expires but you would be legal otherwise. Even just renewing without any sort of review takes more than 6 months so if you wait until the last day to renew, you will be illegal for ~3-6 months.
The difference is that the MAJORITY of Europeans, Asians and African people come here legally or are truly refugees and then their status changes or they don't know how to do the paperwork (especially a problem in African communities where people don't know how to read, let alone read English).
The people in detention centers on the other hand are only there temporarily unless they have clear gang affiliations. They are either detained crossing the border or are voluntarily surrendering at a port of entry. That would be primarily South American people because that's the only border people do this en masse. The detention centers only keep people for a couple of days (a lot of people from India, Pakistan and the Middle East have embedded themselves in the migrant caravans) and then release them into the interior with a court order to come back and make their case a certain time in the future, most end up never showing up and THEN they become illegals.