Both marble and alabaster have been used since antiquity for sculpture and other artwork. In ancient times the alabaster used by artisans was a form of calcite, and essentially was the same thing as marble. Now when artists use alabaster they're working with gypsum, a material that has some similarities with marble, but some differences as well.
Weight and Origins
Gypsum, in the form of alabaster, is much lighter than marble. Alabaster weighs 64.9kg. per cubic foot while marble weighs 73.5kg. per cubic foot. Alabaster is a chemical sedimentary rock, which means it was made of detritus precipitated from a body of water. Gypsum alabaster is in fact an evaporite of salt, and was formed out of the evaporation of marine water.
Marble is a metamorphic rock, which was formed out of another sort of rock due to the extreme heat and pressure in the Earth's crust. Some of the oldest alabaster is found to Ordovician depths in the Earth, which means it was laid down 500 million years ago.
Alabaster is softer than marble --- which is also considered a soft mineral. Alabaster is 2 on the Mohs scale while marble is 3. This means that marble is twice as hard as alabaster. Marble is just hard enough to be used for monumental sculpture and buildings. Alabaster can be scratched with a fingernail and can be easily carved with a hand saw.
Alabaster can be so translucent that it was used for windowpanes before glass was perfected. Light does sink into marble and then retursn to the eye, giving the stone an unmatched luminescence, but marble never becomes as translucent as alabaster.
Cost, Occurrence, Durability
Alabaster is and has always been less expensive than marble. Though both are found all over the world, alabaster is more common in North America than marble is. Marble is usually named after the place it comes from, such as Carrara, but alabaster isn't. Marble statuary can be kept out doors, even though it must be cared for to avoid corrosion. Alabaster statues and figurines are too fragile to be kept outdoors.
Though sculptors and artists prefer white marble, marble can be used in any and every other colour for countertops, tabletops, walls or floors. Except for the rare black alabaster, alabaster must be pure white. If it's not pure white it can be ground up for use in plaster of Paris or stucco, or as filler in paper or rubber. After a time, some alabaster can develop brownish veins or clouds, which lessens its value.