Milli:
A good resource for questions like this is the free online gem index provided by Rings & Things.
Our Gem Index is regularly updated as we learn
new things. We recently added a group of new agates and jaspers. The Gem Index is also available as a print version but, of course,
that's not automatically updated.
The free on-line gem index is available from our home page (rings-things.com) or directly at http://www.rings-things.com/gemstone/index.html click here for index
The printed Gemstone Beads Index, stock #68-100-01, can be ordered for $12.
The index confirms the other answers that both kinds of carnelian (multi-color carnelian agate and red carnelian) are microcrystaline quartz. The all red carnelian is usually enhanced to become uniformly red.