The $2,200 is indexed for inflation from here on. The $500 credit for other dependents is not refundable and is not indexed. Both credits are figured on Schedule 8812.
The credit first reduces the tax you owe. If it reduces your tax to zero with credit left over, up to $1,700 per child can come back to you as a refund. That refundable part is figured from your earned income, so a family with very little earned income gets little or none of it. A family with two children and $3,000 of tax uses $3,000 of the $4,400 credit and can receive the remaining $1,400 as a refund.
The phase-out is gentle and most families never reach it. A couple with two children loses $50 for every $1,000 of modified adjusted gross income above $400,000, so their $4,400 credit is gone at $488,000. The thresholds are not indexed. More on phase-outs for higher earners.
The $500 credit for other dependents covers dependents who are not qualifying children for this credit: a 17- or 18-year-old still at home, a college student, a parent you support, or a child with an ITIN. It only reduces tax; it is never refunded.
Behind the scenes
Every Social Security number on a return is matched against Social Security’s records when the return is filed. A card that says “Not valid for employment” disqualifies the child from the $2,200 credit even though the child is a legitimate dependent. We check the card, not just the number, because a return that claims the wrong credit is either rejected or quietly reduced by the IRS months later, with a letter.