I'm a programmer and therefore used to the differentiate between parameters and arguments. For programmers, parameters are placeholder variables used to store the inputs of functions; arguments are the concrete values passed to a function application.
Example: In the program …
let f(x,y) := ...;
let z := 3;
let z := f(1+2, z);
… function f has the parameters x and y. The concrete values 1+2 and z (that is 3) are arguments of f.
However, in math it seems like argument is used to describe any free variable of a function (see *), not the value given to that variable during an application of that function. That is, the function $g:(u, v)\to\ldots$ has the arguments $u$ and $v$.
When applying $g$, how would I refer to the things $g$ is applied to? That is, in the application $g(1+2, w)$ what is the name of $1+2$ and $w$ or the tuple $(1+2,w)$?
* From Wikipedia »Argument of a function« (2019-09-16)
an argument of a function [...] is also called an independent variable. [...] For example, the binary function $f(x, y) = x^2 + y^2$ has two arguments, $x$ and $y$.
However, the same article also says
an argument of a function is a specific input to the function
but this definition contradicts the definition as an »independent variable«. I ignored the second quote as the rest of the article was just about the first quote.