From this not seasonally adjusted data, Q2 GDP merely dropped 1-4305/4674=8% QoQ? What makes this number to be so different from the 32.9% decline they published today supposedly calculated form the seasonally adjusted GDP data?
As Fred dataset clearly states the second series in quarterly series at an annual rate where the $32.9\%$ change is calculated just as the difference from preceding quarter. The annual rate change from preceding quarter is calculated differently than quarter-on-quarter rate. You can review the formulas fred uses here. Most of the discrepancy between the numbers can be attributed to that.
the seasonal adjustment is done by Fed using algorithms not by calculating quarter-on-quarter value so a discrepancy might creep already just from different method of seasonally adjusting the data although that should not be excessive.