For rocks, Carnelian and Cornelian are the same.
M F Christensen's American Cornelian was oxblood -- those are the famous bricks. I believe that Akro called their bricks Red Striped Carnelians in the 1910's. So those are different from when Akro used the Carnelian name again in the 1930's.
Akro's Cornelians from the 20's look like so -- not quite a slag but similar:
So you can see the difference between that and the Akro Carnelian of the 30's.
Akro's Moss Agates came in different patterns: Swirl and cork as well as patch. Collectors call the swirly and corky ones different things now -- Ades, Aces, Ringers, Blue Eggyolks, etc. -- but for Akro they were Moss Agates.