operands function works differently inside a procedure

Question

Let's define a procedure

[> f:=proc(s)
     s:={1}: {op(s),2};
   end proc:

then

[> f('s');
                            {2, {1}}

but

[> s:={1}: {op(s),2};
                             {1, 2}

So why do we have a different result?
Using a local variable we can get the expected result though:

[> f:=proc(s) local S;
     S:={1}: s:=S; {op(S),2};
   end proc:
   f('s');
                             {1, 2}