Those are what are called Altered Plates. The original 5¢ stamp and a 1¢ picturing John C. Calhoun (#6,7 and 14, which was never issued) were designed and printed by De La Rue in London in 1862. By the next year it was necessary to raise the postal rate, so the Confederate Posties asked De La Rue to come up with a new set. As time was of the essence, it was decided to simply alter the plates (hence the name) from 1 to 2¢ and 5 to 10¢ respectively.
The plates were sent back to Richmond but were never used. Could be delivery was too slow (no Fedex). I have read a story where Mrs Davis disapproved of the portrait on these stamps because she though it made her husband look too much like that Lincoln guy. I've read of rumours during the war that Lincoln and Davis were actually related, simply because there was a slight physical resemblance.
So other stamps were designed (CSA#8 and #9) and the altered plates were filed away.
The aforementioned August Dietz, the Father of Confederate Stamp collecting, reportedly found the 2¢ plate in the 1920s and produced a nice emerald green stamp.
I've got one in my collection...
Other printings, of both stamps in various colours occurred during the 20th century. There's an image of a sheet of 9 of the Davis on the Confederate Forgery article you posted a link to, which were printed in 1918. I think some others were printed in the 1950s for a philatelic exhibition.
The quality of these printings varied widely which would account for the last two you posted. I've got a couple with some major ink hickeys. Lack of quality control.
So there you go. Worthless, really, but I think they are full of history, and kind of fun to add to a CSA collection.