Green calcite is calcite that happens to be green, and setting out what that does and does not mean is the useful job for this entry.
Calcite is calcium carbonate, and pure calcite is colourless. It is one of the most promiscuous minerals in the world for taking up impurities and inclusions, so it occurs in essentially every colour: honey, blue, pink, orange, red, black and green. Green calcite generally owes its colour to traces of copper or to fine inclusions of a green mineral such as chlorite. Two green calcites from two localities may be green for entirely different reasons, and neither is a distinct mineral variety in the way that amethyst is a variety of quartz with a defined cause of colour.
That is worth stating because of how the modern crystal market names things. A colour prefix attached to a common mineral name produces a stone: green calcite, blue calcite, orange calcite, each with its own listing, its own price and, in many catalogues, its own set of attributed properties. Mineralogically these are one substance with different impurities, and the properties assigned to them differ because the catalogue needed them to differ, not because any tradition distinguished them.
The atlas gives green calcite its own entry because the market and the modern literature treat it as one, and records here that the distinction is commercial rather than mineralogical, and that the attributions attached to it are twentieth century and later. Calcite of any colour is soft, at three on the Mohs scale, and it dissolves in weak acid.