The astral plane as a described region with subdivisions, inhabitants and rules of travel is a product of the late nineteenth century. Charles Leadbeater's short book of 1895 laid out seven subplanes, the kinds of entity found on each, and what a trained clairvoyant would see, and that scheme is the direct ancestor of essentially everything written on the subject since, including material that presents itself as much older.
The vocabulary was borrowed from India. Theosophy took terms for the sheaths and worlds of Vedantic and tantric literature and mapped them onto a Western frame, which is why the same authors use kama-rupa and etheric double in the same paragraph. The Sanskrit sources are being used as raw material for a new system, not summarised.
A practical literature followed. The Projection of the Astral Body by Sylvan Muldoon and Hereward Carrington, published in 1929, gave techniques and case reports and set the template for a genre that is still being written. From the 1960s researchers approached the same experience as a psychological question, under the name of the out-of-body experience, and the resulting work by Charles Tart, Susan Blackmore and others is a separate and better-evidenced literature that reaches quite different conclusions about what is happening.