How to explain precisely the distinction between "using the letter $x$ as an unknown" and "using the letter $x$ as a variable"?
Is it a syntactic difference? a semantic one?
is the difference pragmatic in nature ( relative to the intentions of the person that uses the symbol : relative to "I want to find the value of $x$")?
Can I explain it in the following way :
$x$ is an unknown iff $x$ appears in a conditional equation
$x$ is a variable otherwise ( identity, defining formula of a function, etc?)
In a book ( Mathématiques de A à Z, Georges Alain , 1999) I read : " A variable is a number to which one can attribute any value one wants. An unknown is a number the possible values of which we are looking for. The oppositite of " variable" is " constant" , the opposite of " unknown" is " given").
In case this distinction would be outdated or out of use, what was the traditional explanation of this distinction?