I think you're on target.  I'll have to brush up on these if I run into any, but my recollection is that the two periods are independent.

It might be helpful to run through the 2021 form 7202 (draft instructions are out now):

https://www.irs.gov/pub/irs-dft/i7202--dft.pdf

https://www.irs.gov/pub/irs-pdf/f7202.pdf

FFCRA happens in parts I & II.  ARPA happens in III & IV.

Rick