Child Tax Credit vs Credit for Other Dependents

I have 2 children and they were categorized differently on my 2020 tax return. My 4-year-old got a check in the "child tax credit" column but my other child (born August 2020) got a check in the "credit for other dependents" column. Is this because the baby did not live with me for half the tax year 2020? Also, for the recent child tax credit payments that started this month, I only received payment for one child though based on our AGI we are eligible for payments for both children. Is this for the same reason? Will the credit for my newborn come in my 2021 return? Thank you!