Quotes, sayings, aphorisms, maxims. What's the difference between all these, especially aphorism vs. maxim?
An aphorism is a synonym for a proverb, that's also short and to the point. Usually, it's supposed to impart some important moral lesson. Here's a well-known example:
A bird in the hand is worth two in the bush.
A maxim is a slogan or a personal prescription for some generality of life; importantly, it does not have the same moral connotations as an aphorism. Maxims can be downright dangerous; consider
Four legs good, two legs baaaddd.
from the famous Orwell satire Animal Farm, a phrase famous for connoting the kind of totalitarian mindset required for enforcing the simplistic sociology Orwell found in communism.
A big difference between the two words is that aphorisms need be drawn from society somehow -- they are known to people other than yourself, they are received wisdom. In contrast, one can have personal maxims; it's fairly common nowadays for people to tattoo such on their bodies, things like "Faith and Family" in elaborate script to apparently remind them how to live.
Aphorism's are western and maxim's are more eastern. And contrary to the previous answer, maxim's are commonly deeper than aphorisms.