True, but they are both part of the disaster triumvirate of fEMA, SBA, and ACE (Army Corps of Engineers). To file a claim with the latter two, they require you to first file a FEMA claim. FEMA vets the disaster, date, and your zipcode. They then assign a DR number which is a requirement of the other two and yes, separate, agencies.
So it is not FEMA’s fault that SBA has run out of the funding authorized by Congress.
SBA is not broke. Just makes for a good headline.