"Chalk" is a variety of "limestone" which is composed primarily of the shells of single-celled, calcium carbonate secreting creatures. Think about this next time you use chalk - that white stuff all over your hands is actually countless individual shells, each microscopic in size and the former home of a living being.
Coral rag is a rubbly limestone composed of ancient coral reef material. The term also refers to the building blocks quarried from these strata, which are an important local building material in areas such as the coast of East Africa and the southeastern United States littoral (e.g. Florida, Bermuda).
Fossiliferous limestone is any type of limestone, made mostly of calcium carbonate (CaCO 3) in the form of the minerals calcite or aragonite, that contains an abundance of fossils or fossil traces. The fossils in these rocks may be of macroscopic or microscopic size.