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pi is a symbol that we all use and it looks something like this....
To "represent" something or someone IS a symbol's purpose. To empower the wielder of the symbol with what the symbol represents.
There is no intrinsic difference. Either can be named using the names of any two points on them, or using any letter or symbol of any alphabet - including symbols that you have made up.
a symbol that means there is more than enough of something
The verb of symbol is symbolise. As in "to symbolise something".