Vedantic thought lays a second, coarser scheme over the five koshas: three bodies, or sharira, the gross, sthula sharira, the subtle, sukshma sharira, and the causal, karana sharira. Pranamaya, the vital sheath, belongs to the subtle body along with the mental and wisdom sheaths, distinguishing it from Annamaya, the food sheath, which is identified with the gross body alone and left behind at death.
This placement is why Pranamaya is treated in the tradition as carrying forward at death rather than dissolving with the physical form: the subtle body, prana included, is said to persist and transmigrate until liberation, while only the gross, food built body decays.
Pranamaya's link to prana, the breath, also connects it to yogic breath practice more directly than the other sheaths; controlling the breath through pranayama is described in the tradition as a way of working on the vital sheath specifically, calming and directing the energy that in turn steadies the mental sheath above it. Twentieth century Theosophical writers later adapted kosha vocabulary into their own, differently bounded scheme of subtle bodies, a distinct Western system built from borrowed terms rather than a continuation of the Vedantic teaching.
Sources The Principal Upanishads with Rainbow Body: A History of the Western Chakra System from Blavatsky to BrennanKurt Leland