Aragonite is calcium carbonate. Calcium carbonate is its chemical name. Aragonite is a geological form that is primarily composed of calcium carbonate.

The main difference is porosity. Limestone gas been compressed over million of years. All of the tiny pores that are typical of LR have been compressed into something that is more solid. Aragagonite is relatively young, in geological terms. It was never deeply buried under other sediments and therefore retains its porosity.

Gary