These are American shad, with blueback herring and some hickory shad mixed in (not to be confused with gizzard shad or threadfin shad - totally different species). They are anadramous fish, like salmon, that grow in the ocean, but come back to the river where they were born to spawn.
A lot of people fish for them in the Tailrace canal in Moncks Corner, SC because they pile up below the dam (to Lake Moultrie) as they try to migrate up river. The standard rig there for the shad is either one or two 1/8 oz jigs heads with 2" chartreuse curly tail grubs. Other colors will work, but chartreuse is the most popular. Depending on current and tackle, some folks also add a split shot or two to get the grubs down deeper. Personally, a single 1/8 oz jig and grub on an ultralight rod works great for me. These are real strong fish and a blast to catch!
The shad average about 1 to 4 pounds, but the herring are much smaller, maybe 10 to 12 inches. The sabiki rigs are more effective for collecting herring, but will also catch a few shad. Both herring and shad make excellent catfish bait. Some folks put some in the freezer to use later in the season.