Mathematical notations are usually called symbols in the large, yet particular symbols seem to be blessed, they are often called signs ('equals sign', 'multiplication sign', ...). Is there a linguistic justification for this, or more precisely, is there a generally agreed difference between symbol and sign?
Among the various words descended from the Latin "signum," an identifying mark, are signature, signify, assign, ensign, SIGN, all generally having to do with marking something with a practical label. For instance, a signature marks the authenticity of a document. A stop sign marks the intersection with a government mandate to bring your vehicle to a halt. A naval ensign is a flag flown from a ship to declare its military significance. The interpretation of a sign is usually assumed to be literal.
The word SYMBOL descended from the Greek "symbolon," sym, from syn = together, bol = thrown, hence thrown together. Symbol came to mean a representation of an idea. It's interpretation was intended to be metaphoric, not literal.
This distinction between conceptual ideas and practical operations follows logically to mathematics, where the overarching concept of notation as representational is called symbolic. Whereas the mark specifically directing each operation is typically called a sign.
They are both used to describe the same thing:
1)Symbol: A pattern or image used instead of words.
Example:"+" is the symbol for "plus"
2)Sign:When used with a name, it means a symbol used instead of words, such as the "Stop" sign.
Example: "%" is the percent sign.
Further hypothesis(But no source) :They can both be used for the same thing if and only if the word used can the word "sign" with it. For example
Sigma is not pronounced with a sign but is a symbol. So all signs are symbols but not all symbols are signs.