Nice finds and great pictures, Rob, Thank You!
Very interesting and pretty quartz crystal cluster in the 3rd picture, and nice fossil in the last pic. Great place to rockhound, especially if you are looking for knapping material or artifacts.
Yes, folks would rather call it agate than chert, but you are correct and technically the formation is chert, even though some of it is definitely high grade enough to call agate. I think if you're in South Carolina it's called chert but in Georgia it's agate. 
That huge outcropping on the Savannah River is called "Allendale Chert" and is part of the Coastal Plains Chert that outcrops here and there from southern Virginia, thru NC SC and GA and ends somewhere in Alabama. There's another big outcrop on the Flint River south of Atlanta, and guess what they call it. Yep, flint. 

I haven't been down there since they cleared it about 10 years ago. Glad you're checking it out!