No, these are separate. One is an automatic penalty if you fail to pay as required. $35 is optional reinstatement fee. It's all here:
If the Minimum Payment Due is not paid by the
Closing Date of the billing period in which it is due,
you will forfeit the Points you received for eligible
purchases during that billing period. For example,
if your billing period closes January 15 and the
minimum payment for that billing period is due on
February 10, and you do not make that minimum
payment due by the close of your next billing period
on February 15, then you will not earn Points for
spend in the billing period ending February 15.
You may reinstate those Points within the next 12
billing periods if your Card Account is not past due
and you pay a $35 fee.
https://www.americanexpress.com/cont...03-28-2019.pdf
I have to be honest I've been with Amex since 2004 and didn't know about the forfeiture of points on a late/missed payment. Luckily I guess I have never done that with my Amex (I have with other cards). If it's a rare occurrence you'd hope CS could waive that fee.