The earned income tax credit and the child tax credit are two different things.
Until we redefine birthright citizenship, children born here are considered American citizens and are issued a SSN which is required to qualify for a CTC. If their illegal immigrant parents were deported like they're supposed to be, they wouldn't be here earning a living, filling out 1040s, and claiming tax credits.
The only difference between the two is income level.
Other than that they are identical. And payable.
Either as a direct credit to taxes owed, or a check when no taxes are owed.