A saying is a short, commonly known expression which usually offers advice or wisdom. Proverbs, mottos and maxims are types of sayings.
A proverb is a piece of common-sense wisdom. ie: "nothing ventured, nothing gained"
A motto is a sentence chosen to represent the ideals of an institution or company. ie: "Subway, eat fresh" (The Subway motto)
A maxim expresses a general truth or prescribed rule of conduct. ie: "actions speak louder than words"
I hope I could help.