Calcite and aragonite are polymorphs meaning they have the same chemical formula, but different crystaline structures. Aragonite is meta-stable and about 1.5 times as soluble as calicte in seawater. There are a large variety of calcifying organisms ranging from corals to coraline alage and many others.
In order to calculte CO2 in seawater you must measure at least 2 of the 4 carbon parameters (total alkalinity, total CO2, pH, and pCO2) from those two you can use a freely available program such as CO2sys to calculate the others, as well as the concentrations of the individual ions.
Aragonite is relatively high temperature mineral than calcite |.
Apart from Calcite |, there are other three more polymorphs as: Calcite ||, Calcite |||, and vaterite. However, || and ||| are structural modifications of calcite lattice and are stable only under pressure in excess of 15Kbars at 300 degree celcius.
Corals r d main aragonites and forams and other species are calcitic.
I want to add this to Pawan Kumar Gautam's and Ryan Woosley's answers:
Aragonite has a stucture that is more resistent to stress than calcite, explaining why organisms that live in high-enegy environments (e.g. corals) prefer aragonite skeletons over calcite. As noted above, calcite is less prone to dissolution, which is why orginsms that live at greater depth (e.g. benthic foraminifera) prefer calcite over aragonite, especially when they live below the Aragontie Compensation Depth.
Bivalves are organisms that use both minerals, building a layer of calcite on the outside of their shell while building an aragonite layer on the inside of their shell where the strong shell closing muscle attaches to the shell.
There is a nice review paper on calcite vs aragonite seas that helps to understand these questions:
Ries, J.B., 2010. Review: geological and experimental evidence for secular variation in seawater Mg/Ca (calcite-aragonite seas) and its effects on marine biological calcification. Biogeosciences 7, 2795–2849. doi:10.5194/bg-7-2795-2010
Biogenic calcite and aragonite are not pure minerals. They have specific chemical contents (organic matrices, Mg, Sr..) characteristic of the organism. Moreover, both polymorphs often co-exist in the same shell or skeleton.
Types of Pteropods also have an aragonitic skeleton. Thus emerged the terminology of Aragonite Compensation Depth (ACD) and Calcite compensation depth (CCD) marking the deepest depths (in oceans) of occurrence of pteropod and foram shells respectively.
Dhunakarasamy, regarding your question: as mentioned by the colleagues above it depends on the organism itself and the environment it inhabits. But you can measure it in the shell material using Raman, or even Confocal Raman spectroscopy. Even shell material, that originally consisted of aragonite can be turned into calcite, for example through heating of the shells. For radiocarbon dating this does not influence the age as long as the heating process was rather quick. For stable isotopes then the oxygen values are shifted. Other elements might differ as well. Just make sure to know some things about your shell before you use it :-)
Aragonite is a polymorph of calcite, which means that it has the same chemistry as calcite but it has a different structure, and more importantly, different symmetry and crystal shapes. Aragonite's more compact structure is composed of triangular carbonate ion groups (CO3), with a carbon at the center of the triangle and the three oxygens at each corner. Unlike in calcite, the carbonate ions do not lie in a single plane pointing in the same direction. Instead they lie in two planes that point in opposite directions; destroying the trigonal symmetry that is characteristic of calcite's structure. Aragonite has an orthorhombicsymmetry (2/m 2/m 2/m) instead of calcite's "higher" trigonal (bar 3 2/m) symmetry.
Should also note that there are density differences. Aragonite has a density of 2.93 g/cc while calcite has a value of 2.71 g/cc. This could be valuable for swimming bivalves (pectinaceans) or for preventing epifaunal bivalves from sinking too deep into the substrate.