In what ways do sentencing philosophies provide different answers to the statement "the punishment should fit the crime or criminal?"
In general, there are four different philosophies regarding the goal of legal punishment. Each one has a different purpose in relation to the idea that the punishment should somehow correspond to the type of crime committed.
The philosophies are:
1) Retribution -- This fits well with that statement. In retribution, the punishment must be proportioned toward "righting the wrong" done to the victim. This may mean "eye-for-eye" type justice, or it may just mean a punishment of roughly equal unpleasantness.
2) Deterrence -- This type of punishment is meant to be unpleasant enough that the criminal is not likely to get out and repeat the offense; likewise, the punishment is supposed to scare other people into not breaking the law in the future. This does not relate to "fitting the crime."
3) Incapacitation -- This, in some ways, is related to "fit the crime." The idea with incapacitation is that by locking someone up they are unable to commit further crimes. In one way it fits the crime because you can lock someone up for a long time if they have done something particularly unacceptable to society, even if what they did was not violent. In another way it "fits the criminal" because you can lock up someone who is a wicked person for a long time for a minor offense in order to keep them from the freedom that would allow them to do something worse.
4) Rehabilitation -- This idea on sentencing posits the idea that even horrible people can be "reformed" through incarceration. Largely regardless of the crime, attempts are made to improve the prisoner enough that, upon release, they will integrate into society. This is not, generally, a "fit the crime" idea.
So, as you can see, only "retribution" really attempts to "make the punishment fit the crime" in an old-school sense.