The West in my experience tends to classify iconography as one of many kinds of religious art.
Some Western art is very much influenced by Byzantine iconography (e.g. the San Damiano cross popular amongst Franciscans:
franciscanfriarstor.com/archive/stfrancis/images/SanDam3.gif). Italy had notable influences from Byzantium through the southern states which had a long Byzantine presence, and also through Florence. Some Renaissance artists, for example Duccio, were heavily influenced by Byzantine iconography, and their works are just as Eastern as Western in appearance. e.g.
upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Duccio_Maest%C3%A0.jpg/800px-Duccio_Maest%C3%A0.jpg
I also notice that Romanesque art is similiar to Byzantine iconography in some respects. e.g.
upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Meister_aus_Tahull_001.jpg/531px-Meister_aus_Tahull_001.jpg
As you may know, Christian art from the start took motifs and templates from Roman Imperial imagery, classical Greek and Roman religion and popular art and ‘baptized’ them as her own. In the Late Antique period iconography began to be standardised, and to relate more closely to Biblical texts, albeit many of the gaps were filled in with matter from popular apocryphal literature. Some of these were eventually weeded out, but some still remain, like the ox and donkey at the birth of Jesus.
After the period of iconoclasm innovation was regarded as unhealthy, if not heretical, in the East, though it still continued at a glacial pace. More than in the West, traditional depictions were often considered to have authentic or miraculous origins, and the job of the artist was to copy them with as little deviation as possible. Very little room is made for artistic license.
One of the main differences between the iconography of the East and West is the manner of identifying a given saint. The West developed a system of attributes for identifying individual figures of saints by a standard appearance and symbolic objects held by them, while in the East they were more likely to be identified by labels of text.
From the Romanesque period sculpture on churches became increasingly important in Western art (the use of monumental high relief or free-standing sculpture never caught on in the East because it was too reminiscent of the pagan tradition of statuary), and probably partly because of the lack of Byzantine models, became the location of much iconographic innovation, along with the illuminated manuscript, which had already taken a decisively different direction from Byzantine equivalents, under the influence of
Insular (Hiberno-Saxon) art and other factors.
Eventually developments in theology and devotional practice produced artistic innovations and new iconic types in the West, but for the most part, painters remained content to copy and slightly modify the works of others, and it is clear that the clergy, by whom or for whose churches most art was commissioned, often specified what they wanted shown in great detail.
Whereas in the Romanesque and Gothic periods the great majority of religious art was intended to convey often complex religious messages as clearly as possible, with the arrival of
Early Netherlandish painting (15th-16th centuries) iconography became highly sophisticated, and in many cases appears to be deliberately enigmatic, even for a well-educated contemporary.
From the 15th century Western religious art gradually freed itself from the habit of following earlier compositional models, and by the 16th century ambitious artists were expected to find novel compositions for each subject, and direct borrowings from earlier artists are more often of the poses of individual figures than of whole compositions.
The Renaissance and subsequent movements pushed for more realism and ‘authenticity’ in Western art - both secular and religious - and the end result were artists like Leonardo, Michelangelo, Tintoretto, and Raphael.
The Reformation, and the iconoclasm of certain circles, soon restricted most Protestant religious painting to Biblical scenes conceived along the lines of history painting, and after some decades the Council of Trent reined in somewhat the freedom of Catholic artists. While the Protestants largely removed public art from religion and Protestant societies moved towards a more secular style of art, The Church continued to promote art with ‘sacred’ or religious content. The Church felt that much religious art in Catholic countries (especially Italy) had lost its focus on the religious subject-matter, and became too interested in decorative qualities.
…every superstition shall be removed…all lasciviousness be avoided; in such wise that figures shall not be painted or adorned with a beauty exciting to lust…there be nothing seen that is disorderly, or that is unbecomingly or confusedly arranged, nothing that is profane, nothing indecorous, seeing that holiness becometh the house of God. And that these things may be the more faithfully observed, the holy Synod ordains, that no one be allowed to place, or cause to be placed, any unusual image, in any place, or church, howsoever exempted, except that image have been approved of by the bishop…