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No map projection preserves the attributes of a globe, which maintains area, shape, distance, and direction. Map projections can preserve one or two of the attributes of the globe, but not all at once. Select a map projection that makes the best sense for your data.
An equal-area (also called equivalent, equiareal or authalic) projection preserves areal relationships; in other words, given any two regions A and B on the Earth and the corresponding regions A' and B' on an equal-area map, the surface ratios A/A' and B/B' are identical (A and B need not have the same shape; shapes A and A' will probably be different).
An equal-area projection is not necessarily equidistant; in fact, in order to preserve area, at any point the scale distortion in a given direction must be the inverse of the scale distortion in the orthogonal direction. For instance, along the Equator in the conventional aspect of Mollweide's projection the horizontal scaling factor is slightly less than 1, and slightly above 1 in the vertical direction; the net effect is making the continents a bit too slender.
