Hasker defines functionalism and its relation to physicalism
This is from Hasker's The Emergent Self, p. 29. I think a big "divide" in the philosophy of mind has to do with the adequacy of functionalistic definitions of, say, propositional states. If some kind of analysis of, let's say, my believing that the Colts will probably beat the Patriots, is available to the materialist, it is probably a functionalist analysis.
On the other hand, if no such functional analysis is available, the materialist will probably not give up, but may go for some kind of eliminativism, or be a nonreductive realist about proposotional attitudes. The first option is implausible to many materialists, the second runs ininto trouble when it comes to finding a causal role for mental states. The second option also makes the mental a mystery from the point of view of they physical, retaining physicalism while giving up on ever really explaining how the mental comes from the physical.
The key idea (of functionalism) is that mental states are defined in terms of the causes that produce them and the effects they produce these causes and effects include sensory stimuli as causes and overt behavior as effects, but also internal states of the organism as both causes and effects of the states in question….These causal-functional definitions do not by themselves entail materialism, but functionalism supports materialism through a two-stage process: First, as a matter of definition, mental states are equated with causal-functional states. Second, it is proposed the scientific investigation will reveal that the state-types that fill these functional roles are physical.