In an ancient industry like quarrying, you can bet there are special terms for various qualities of the rock that aren't taught in geology school. The following are well known among granite and marble quarriers. (And by that I mean commercial granite and commercial marble.)
Granite might look perfectly random, or isotropic, in the way its mineral grains are organized, but the deep intrusions, or plutons, that formed bodies of granitic rock involved the flow of a fluid magma. This may make the various mineral crystals line up more or less in a consistent direction. The second important thing about granite is that as it cools and crystallizes, it shrinks. Thus it's prone to break in sets of joints in one, two or more directions. The last important thing about plutons is that between their deep birth and their current exposure at the surface, a great pressure has been released from them. The plutonic rock responds by cracking apart in exfoliation sheets that are parallel to the ground surface.
The most important direction in a granite quarry is the rift or run, the direction along which the stone splits most easily. That's usually a vertical plane. Next in importance is the grain or direction of second-easiest splitting. That's usually horizontal. These might be reversed, but in either case the rift and grain are perpendicular to each other. The third perpendicular direction, called the hardway or headgrain, is the direction along which it's most difficult to split the stone. It's generally vertical.
Rift and grain are usually related to the flow joints and exfoliation sheets. They're similar in form to the grain of wood, although that arises from very different growth processes.
In the old days a strong rift and grain were essential for a decent granite quarry, so that blocks could be removed suitable for making curbstones and building stones with as little finishing work (dressing, polishing and so on) as possible. (This page from a Massachusetts quarry shows the old-school look of rift-cut granite.) A granite body with weak or no rift was unworkable. Today granite is sawn using diamond-tipped tools, so while rift no longer will make or break a quarry, it is still important for the initial work of quarrying large blocks.
In marble, the direction of rift and grain is usually related to the original bedding of the limestone or, in a well-crystallized marble, the direction of stress during metamorphism. Because marble is much softer than granite, it doesn't really have a hardway.