No, the $8000 limit is combined. If you contribute $4000 to an FSA, the maximum eligible costs that could be applied to the credit is $4000 (resulting in a $2000 refundable credit).
For most people, the credit is a much better deal in 2021 than the FSA, especially if your income is under $125k. The credit is 50% while the FSA will save 22% federal income tax plus 7.65% social security plus 3-10% state income tax. Even in the highest tax states, the federal credit is larger than the FSA savings. Plus, some states have their own credit. At incomes over $125k, the FSA gradually comes to outweigh the credit. Or, you could have an FSA of up to $10,500 instead of claiming the credit against $8000 of expenses. Even so, the credit is better unless your state income tax rate is higher than 8.5%.
However, are you enrolling in an FSA that is not a calendar year plan (like July 1, 2021 through June 30, 2022)? There may be some options here to leverage that span for maximum savings, but it will be quite complicated to work out.
