Found more information in Pub 501

Pub 501 page 11, Citizen or Resident Test says, 'You cannot claim a person as a dependent unless that person is a US citizen, US resident, US national, or a resident of Canada or Mexico, for some part of the year'. It is confusing what 'US resident' means here - it is the 'Resident-alien' definition? Or the immigration definition?

Then, later, on page 19, Taxpayer identification numbers for aliens, it says 'If your dependent is a resident or non-resident alien who does not have and is not eligible to get an SSN, your dependent must apply for an individual taxpayer identification number (ITIN).' With this, it seems that a dependent CAN even be a non-resident alien.

This is very confusing, maybe we should call IRS...