The tradition of the Eastern Church is not to have statues in its churches. A statue occupies three-dimensions of space, unlike a painting, which only occupies two-dimensions (but can create the illusion of a third). Given that the iconographic form, which is the only artistic liturgical tradition that the Eastern Church will permit, seeks to eliminate as far as possible even the illusion of a third dimension, that is depth, it is hard to imagine how statues (in which the third dimension fully exists) could be created in accordance with the iconographic form. The development of statues for churches came in the West in tandem with the desire to create the illusion of space in two-dimensional representations, generally identified with the beginning of the gothic period in about the 12th century. This did not cause the tradition of relief carving to die out in the West. It has always flourished in both Eastern and Western churches
Relief carving in effect, is a monochrome painting in shadow. So although there is a physical deviation from a strict two-dimensional representation not as a statue does, by imitating the three-dimensional shape, but rather by creating the illusion of depth by altering the tone of the shadow. Where the shadow is to be black (or darkest) the cut is deep and the surface angle close to perpendicular to the broad plane of the image. Where a grey or mid-tone is required, the cut is less deep and the surface angle somewhere in between, depending on how dark or light the artist wishes to make it appear. Where the tone required is white (or lightest possible) the surface faces us directly and is parallel to the broad plane of the image.
The conventional classification of relief carving is a division into bas relief (bas in French is low) and alto (ie high) relief. In the first the cut is shallow and there is no undercutting so that representation is never more than half in the round. Alto relief is where there is undercutting and so there are some elements that are carved more than half in the round. Sunken relief, or intaglio, is where the negative space around the figures is flat and the figures are cut out from it below that surface. For more information on this see article here.
Some might point out that the reason we can perceive form in a conventional statue that is not painted, for example all marble is due to shadow too. This is true. But the difference here is that the shadow is revealing is the true shape of the statue, which in turn imitates the idea in the mind of the artist. Whereas, in relief carving it paints, so to speak, the illusion of depth.
As with all these things, the division between the different techniques is never absolute. Bernini, the great baroque sculptor used to deviate from a strict representation of appearances in his statues and exaggerate certain elements by cutting deep into the stone and creating sharper contrast. He would say that as he didn’t have colour to manipulate the gaze of the viewer, shadow was the main tool that he had.
Below and above, Byzantine 10th century, St Demetrios
6th century Armenian, Virgin and Child
The Magi, Amiens Cathedral, 13th century
Station of the Cross: the English artist, Eric Gill, 20th century, Westminster Cathedral