Within a Python scope, any assignment to a variable not already declared within that scope creates a new local variable unless that variable is declared earlier in the function as referring to a globally scoped variable with the keyword global.

Let's look at a modified version of your pseudocode to see what happens:

# Here, we're creating a variable 'x', in the __main__ scope.
x = 'None!'

def func_A():
  # The below declaration lets the function know that we
  #  mean the global 'x' when we refer to that variable, not
  #  any local one

  global x
  x = 'A'
  return x

def func_B():
  # Here, we are somewhat mislead.  We're actually involving two different
  #  variables named 'x'.  One is local to func_B, the other is global.

  # By calling func_A(), we do two things: we're reassigning the value
  #  of the GLOBAL x as part of func_A, and then taking that same value
  #  since it's returned by func_A, and assigning it to a LOCAL variable
  #  named 'x'.     
  x = func_A() # look at this as: x_local = func_A()

  # Here, we're assigning the value of 'B' to the LOCAL x.
  x = 'B' # look at this as: x_local = 'B'

  return x # look at this as: return x_local

In fact, you could rewrite all of func_B with the variable named x_local and it would work identically.

The order matters only as far as the order in which your functions do operations that change the value of the global x. Thus in our example, order doesn't matter, since func_B calls func_A. In this example, order does matter:

def a():
  global foo
  foo = 'A'

def b():
  global foo
  foo = 'B'

b()
a()
print foo
# prints 'A' because a() was the last function to modify 'foo'.

Note that global is only required to modify global objects. You can still access them from within a function without declaring global. Thus, we have:

x = 5

def access_only():
  return x
  # This returns whatever the global value of 'x' is

def modify():
  global x
  x = 'modified'
  return x
  # This function makes the global 'x' equal to 'modified', and then returns that value

def create_locally():
  x = 'local!'
  return x
  # This function creates a new local variable named 'x', and sets it as 'local',
  #  and returns that.  The global 'x' is untouched.

Note the difference between create_locally and access_only -- access_only is accessing the global x despite not calling global, and even though create_locally doesn't use global either, it creates a local copy since it's assigning a value.

The confusion here is why you shouldn't use global variables.