Aragonite has the same chemistry as calcite - it is calcium carbonate (CaCO3). Why is it a different mineral? Aragonite has a different molecular structure - the atoms are packed differently. Different minerals having the same chemical formula are called polymorphs (another good example is graphite & diamond - both C).
The difference in atomic-level packing between calcite and aragonite can be seen at the level of mineral hand samples. Aragonite forms crystals in the orthorhombic class. Many aragonite crystals are acicular (needle-like). Many aragonites form pseudohexagonal crystals (see samples shown below), the result of 6 orthorhombic prisms growing parallel to each other. The sample below looks like a 6-sided crystal (hexagonal), but it's not.
Like calcite, aragonite is moderately soft (H=3), is often clearish to whitish to yellowish, and easily bubbles in acid. Aragonite is a little bit heavier than calcite, due to closer packing of atoms.
Most modern seashells & coral skeletons are composed of the aragonite. Whitish-colored lime sand beaches in the world are aragonitic. Occasionally, "whitings" are seen in shallow, warm ocean environments. Whitings (cloudy, milky seawater) turn out to be loaded with tiny hair-like needles of aragonite.
In the rock record, aragonitic or aragonite-rich sediments convert to calcite over time. Cenozoic-aged carbonate sedimentary rocks are often aragonitic. Mesozoic- and Paleozoic-aged carbonates are almost always calcitic. Many ancient fossils have had their aragonitic shells dissolved away. Ancient shells that were originally calcitic are often still well preserved.
Aragonite (3.4 cm across) showing pseudohexagonal crystal form. From Larimer County, Colorado, USA.
Aragonite (2.1 cm across) - pseudohexagonal, cyclic twinned individual from Spain.
Aragonite (3.4 cm across) - side view of cyclic twinned individual shown above, from Spain.
"Star Aragonite" (4.6 cm across) - cluster of radiating pseudohexagonal, cyclic twinned aragonite masses. From Tazouta Mine, southeast of Sefrou, Middle Atlas Mountains, northern Morocco.
Aragonite ("flos-ferri") from Eisenerz, Styria, Austria.
(Wayne State University collection, Detroit, Michigan, USA)