Illegal immigrant is such a more accurate term than undocumented. Pity it's considered derogatory, nowadays. It really encapsulates the thing in a way undocumented doesnt. I actually think it's a nicer term. It makes clear that the only fault is the illegality of their immigration. Undocumented is just a misnomer. It suggests documentation is available and possible and suggests the crime is in their failure to acquire these unattainable documents. Essentially, one is factual and the other is intentionally misleading.