What is the difference between metaphorical, allegorical, and figurative?
Metaphor comes from the Greek μετά + φέρω ("I carry with") and is a rhetorical figure used to "carry" the meaning of a word into another.
In this case the square is not actually an heart, but can be considered as the "pulsating center" of the town.
Meaning he is sly, not that he is actually a fox.
Note that if you say
that is not a metaphor, but a simile as you are comparing George to a fox, you are not saying he is one.
Allegory comes from the Greek ἄλλος + ἀγορεύω (to speak something different) is in a certain way similar to metaphor, as it expresses a concept using a different word. Contrary to metaphor, however, the shift of the meaning is often deep and hidden (that is probably why in common talk you will be likely to use a metaphor but not an allegory). My English literature is a bit rusty, especially this early in the morning... but I can give you an example from the Italian literature. In the first book of the Divina Commedia, Dante meets three beasts blocking his path: a lion, a lonza (some kind of leopard), and a she-wolf. These are allegories for the sins that Dante thinks can block the path of man towards (religious) liberation and work against ethic: pride, lust and greed.
It is important, here, to consider that in this case you actually have two meanings: the literary meaning and the hidden meaning. Dante is walking through a forest and he finds three beasts that block his way. You can stop there and just take this as the meaning. Or you can understand the image the author is conveying and see that the forest represents life and the beasts are capital sins. On the other hand, in the example of metaphor I wrote before you only have one meaning. Unless you are very naïve (or imaginative) you will never think there is a heart in the center of the town!
Finally, figurative refers in general to figures of speech, such as allegories and metaphors, and many others.
Metaphor in casual usage has come to mean figurative, that is, a non literal statement. However metaphor has a much tighter meaning that that. Allegory is a story where there are some obvious parallels and lessons from the comparitive situation.
There is a progression of comparative figures of speech in English, each stronger than the previous. They are simile, metaphor and hypocatastasis. Here are examples of a mom talking to her child:
Your room is like a pigsty, clean it up. (Simile, the comparison is made with "like" or "as".) Your room is a pigsty, clean it up. (Metaphor, a declaration that the room "is" a pigsty.) "Clean up this pigsty!" (Hypocatastasis, the comparative word is used in substitution.)
In all cases the meaning is "your room shares some characteristics of a pig sty."
With apologies to our porcine friends.
All three are about nonliteral readings.