Crushed coral can be many different things, but normally it contains exactly what it says - crushed coral. Old dead coral skeletons of any age - could even be ancient fossilized corals.
It works fine as a substrate in a marine saltwater tank, although it has a tendency to trap wastes and uneated food particles due to it size, shape and overall structure when placed on the bottom of the tank.
Aragonite is "new" or recent dead coral skeletons or a mix of these dead skeletons, and ocean born limestone or oolite sand. It's a term applied to the types of eroded sands/gravels that are found near the base of recent coral reefs - not prehistoric material or fossil material. It is made of the same materials that the reef itself is made of.
I'm sure some if it is pulled from the sea in it's natural grain size/state, and some other forms of aragonite are mechanically "crushed" and sifted to within a certain grain size grade, and marketed as such,
Aragonite exits in various "grain" sizes from large chuncks to very tiny sand particles. It's made of calcium carbonate which many feel is a benefit in a marine tank. Others do not feel this way and believe that any sand of any origin is fine to use, as long as it has the proper mixture of grain sizes.
DSB using these types of sands work wonders in most every tank. Most every.
There's more to it than just the substrate.
I've used both CC and DSB - and I can say the DSB is much better and my water tests are proving this to me.
Sorry Stacy but I have never heard of aragonite itself leading to alage problems, but certainly do agree with you that the time to make the swap out in the tank is when you have the least number of fish or inverts in such tank.
Source: Dr.Robert J. Goldstein - Marine Reef Aquarium Handbook