To the answer up here (so good answer about 3 shariras), you can add to read this another answer about 5 koshas.
Annamay Kosha : Meaning 'Food Sheath', is the physical body, with hands, eyes, the body which has a name and dies. This is the gross,
physical body. This is the sheath of the physical self, named from the
fact that it is nourished by food.
Pranamaya Kosha : Meaning 'Life Air Sheath', contains the word Prana, which holds together the mind and body, its one physical
manifestation is the breath.
Manomaya Kosha : Meaining 'Mind Sheath', the mind with five sesory organs are the physical manifestation of this Kosha.
Vijnanamaya Kosha : Meaning 'Intellect Kosha',composed of Vijnana, or intellect, the faculty which discriminates, determines or wills.
Anandamaya Kosha : Meaning 'Bliss Sheath', composed of ananda, or bliss,In deep sleep, when the mind and senses cease functioning, it
still stands between the finite world and the self. Anandamaya, or
that which is composed of Supreme bliss, is regarded as the innermost
So, Stula Sharira should be equivalent to Annamaya Kosha, plus most gross part of Pranomaya kosha related to air and breathing. Then Sukshma Sharira should be the more sublte prana of Pranomaya Kosha, Manomaya Kosha and a very big part of Vijñanamaya Kosha, all together
There is a part of Vijñana (most subtle part), where there is karmaShaya, were samskaras are stored, providing cause to rebirth and having pendent experiences (off topic, same karmashaya Patanjali says Ishvara has not). That subtle part, together with Ananandamaya Kosha, should be equivalent to Karana Sharira
All this is like comparing kilometer with miles, just different ways of measure how human is made about. Good question