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There basically no difference. Indeed, if you look at the source code of the __call__ method of formula by typing:

sage: formula.__call__??

you can see that there is :

return self._parent._call_element_(self, *args, **kwds)

So, if you look at the _call_element_ element of the parent of formula (chich is the symbolic ring) by typing:

sage: SR._call_element_??

besides some deprecation warnings, there is:

return _the_element.subs(d, **kwds)

There basically no difference. Indeed, if you look at the source code of the __call__ method of formula by typing:

sage: formula.__call__??

you can see that there is :

return self._parent._call_element_(self, *args, **kwds)

So, if you look at the _call_element_ element of the parent of formula (chich (which is the symbolic ring) by typing:

sage: SR._call_element_??

besides some deprecation warnings, there is:

return _the_element.subs(d, **kwds)