You are confusing 2 credits. There is no Child and other dependent care credit. But there is a credit for other dependents who do not qualify for child tax credit. They are often children over age 17 (23 if a full time student).
Then there is the credit you are interested in—the credit for child and dependent care. If you have a FSA you get credit for $6,000 of expenses. No additional expenses are deductible. If no FSA your expenses are limited to $3,000 ($6,000 for 2 or more children). Note that you don’t get a $6,000 credit for $6,000 of expenses. Your credit is calculated on the basis of that expense.
