According to a Wikipedia article on the subject, in Herbert B. Enderton's book Computability: An Introduction to Recursion Theory (2011), even if nowhere else (no other reference is given, and I've never seen the usage):

If is a partial function on and is an element of , then this is written as and is read as " is defined."

If is not in the domain of , then this is written as and is read as " is undefined".

In the parsed expression there is indeed no difference between functions and symbols, nor between functions/symbols defined in mathjs or in your scope. Some tips:

• You can recognize function calls like sqrt and asin from symbols because they are defined as a FunctionNode having a property .fn being a SymbolNode with a .name property like sqrt or asin. You can use the third parent argument of node.traverse(function (node, path, parent) {...}) to check that.
• Whether something is a built-in function of mathjs can be verified by checking whether say math.asin and math.pi are defined.
• It is possible that a symbol is a unit like inch or millimeter, which will be resolved by mathjs when evaluating. To verify that, you can check the symbol against math.Unit.isValuelessUnit(name), which returns true for valid unit names.
• Not sure if relevant to you, but there are two static functions FunctionNode.onUndefinedFunction(name) and SymbolNode.onUndefinedSymbol(name) which can be overwritten to customize what to do when an undefined symbol is encountered whilst evaluating. I see these functions are not documented, I'll add them to the docs.