The Astral plane is non-physical. It can be thought of as the template for what is manifested in the physical. But it is also a realm in itself that one can operate in. The Spiritual plane is beyond a need for form and looks much less like the physical world than the astral does. Each of these major planes can again be divided up, as mentioned.
Various traditions use different names for the different sub-divisions.
One's physical body has counterparts existing in different planes. The manifestations in the higher planes are often referred to as subtle bodies. In various traditions one would refer to an etheric, an emotional, and a mental body as part of the physical plane, and other subtle bodies as part of the higher planes. The ones closest to the physical are roughly in the shape of the physical body, and act as templates, governing the state of the physical body. The physically oriented subtle bodies are intimately tied to the physical body.