An "un-strict" identity statement would be assymmetrical, for example: rain is identical to bad weather, but bad weather could be rain, sleet, snow, etc.
Identity theory is deemed to be contingent because of the history of the theory.
if minds are identical to brains, then brains are identical to minds.
Strict identity statements are therefore logically symmetrical.
To answer what it is to be in pain, an identity theorist might look up you in a table and find the corresponding physical properties of the brain, or simply the latter, and tell you that to be in pain is to have a particular physiological state.
But does that tell us all there is to know about pain? follows is my essay on this topic: Central state materialism, the dominant branch of identity theory, grew out of a desire in philosophy to explain mental phenomena in terms of the material sciences, which in turn was a result of the growing potential in the mid-20th century of the neurosciences. Place made the extraordinary claim that mental processes can be identified with brain processes in the same way that lightning can be identified with an electrical discharge; when we speak of a thought and of a particular brain state, we speak of exactly the same thing but in different terms.
For example, I might refer to "the table", by which I mean an object with legs on which I can rest other objects; I might also refer to "that lump of wood", by which I mean an object created out of pieces of wood that sits in my room.
Though each statement appears to refer to different physical concepts, they each refer to the selfsame object, and so a CSM can claim that one can reduce all mental concepts to material concepts, even if this seems counter-intuitive.
For example, if one part of my brain is damaged, my brain will often route around this problem, resulting into two different brain states for ostensibly the same mental state.
The context of a mental state also seems important, since the mental state of an experience of red may result in an entirely different brain state if I am feeling hot or cold (not least because of the related symbolism).