What is the difference between limestone, lime and quick lime?

Calcium carbonate is the name of a chemical substance , CaCO₃.
Ground oyster shells are a natural product mainly containing CaCO₃, along with other minor ingredients.
Limestone is a sediment mineral composed mainly of calcium carbonate, very similar to oyster shells.
Chalk (Blackboard chalk is NOT made of chalk!) is a form of calcium carbonate, having the same chemical composition as ground calcium carbonate, limestone, marble, and precipitated calcium carbonate.

Horticultural lime, also called hydrated lime or Ca(OH)₂ is produced by adding water to CaO.

Quick lime is CaO, a very aggressive substance. It is produced from CaCO₃ containing limestone or shellsand by heating it to 1200°C, hereby CO₂ is driven off the CaCO₃ molecule, leaving CaO.

The material that is used in the mushroom industry as a casing ingredient is always some form of calcium carbonate, CaCO₃: either ground chalk, ground limestone or ground shellsand.