I wrote a sample code below:

set(var "ABC")


macro(Moo arg)
message("arg = ${arg}")
set(arg "abc")
message("# After change the value of arg.")
message("arg = ${arg}")
endmacro()
message("=== Call macro ===")
Moo(${var})


function(Foo arg)
message("arg = ${arg}")
set(arg "abc")
message("# After change the value of arg.")
message("arg = ${arg}")
endfunction()
message("=== Call function ===")
Foo(${var})

and the output is:

=== Call macro ===
arg = ABC
# After change the value of arg.
arg = ABC
=== Call function ===
arg = ABC
# After change the value of arg.
arg = abc

So it seems arg is assigned the value of var when calling Foo and ${arg} is just string replaced with ${var} when calling Moo.

So I think the above two quotes are very easy to make one confused, although the official documents also said that:

Note that the parameters to a macro and values such as ARGN are not variables in the usual CMake sense. They are string replacements much like the C preprocessor would do with a macro. If you want true CMake variables and/or better CMake scope control you should look at the function command.

UPDATE (1/29/2021)

Add the following statement after the statement Moo(${var}) to make the difference between macro and function even more clear.

message(${arg})

This statement will print out abc.

In other words, function pushes and pops new variable scope (variables created and changed exist only in the function), macro does not. However, you can override the function default behaviour with the PARENT_SCOPE parameter of the set command.

The cmake documentation you quoted is so misleading that it's basically wrong. It should be clarified/fixed like this:

• macro: when it is invoked, the commands recorded in the macro are first all modified before any is run by replacing formal parameters (${arg1}) with the arguments passed.

cmake --trace-expand shows exactly what happens.

The cmake 3.13.3 doc hasn't changed compared to 2.8.12 with respect to this.

The macro expansion, answered by Yantao Xie really opens my eyes!

I also found the tutorial below comes with some concrete examples, which is helpful to understand the variable scope concept.

Cited from Learn cmake in 15 mins:

In CMake, you can use a pair of function/endfunction commands to define a function. Here’s one that doubles the numeric value of its argument, then prints the result:

function(doubleIt VALUE)
math(EXPR RESULT "${VALUE} * 2")
message("${RESULT}")
endfunction()


doubleIt("4")                           # Prints: 8

Functions run in their own scope. None of the variables defined in a function pollute the caller’s scope. If you want to return a value, you can pass the name of a variable to your function, then call the set command with the special argument PARENT_SCOPE:

function(doubleIt VARNAME VALUE)
math(EXPR RESULT "${VALUE} * 2")
set(${VARNAME} "${RESULT}" PARENT_SCOPE)    # Set the named variable in caller's scope
endfunction()


doubleIt(RESULT "4")                    # Tell the function to set the variable named RESULT
message("${RESULT}")                    # Prints: 8

Similarly, a pair of macro/endmacro commands defines a macro. Unlike functions, macros run in the same scope as their caller. Therefore, all variables defined inside a macro are set in the caller’s scope. We can replace the previous function with the following:

macro(doubleIt VARNAME VALUE)
math(EXPR ${VARNAME} "${VALUE} * 2")        # Set the named variable in caller's scope
endmacro()


doubleIt(RESULT "4")                    # Tell the macro to set the variable named RESULT
message("${RESULT}")                    # Prints: 8

Both functions and macros accept an arbitrary number of arguments. Unnamed arguments are exposed to the function as a list, through a special variable named ARGN.

Here’s a function that doubles every argument it receives, printing each one on a separate line:

function(doubleEach)
foreach(ARG ${ARGN})                # Iterate over each argument
math(EXPR N "${ARG} * 2")       # Double ARG's numeric value; store result in N
message("${N}")                 # Print N
endforeach()
endfunction()


doubleEach(5 6 7 8)                     # Prints 10, 12, 14, 16 on separate lines

Another notable difference between function() and macro() is the behavior of return().

From the cmake documentation of return():

Note that a macro, unlike a function, is expanded in place and therefore cannot handle return().

So because it is expanded in place, in a macro() it returns from the caller. While in a function it just exits the function()

Example:

macro(my_macro)
return()
endmacro()


function(my_function)
return()
endfunction()


my_function()
message(hello) # is printed
my_macro()
message(hi) # is not printed