The "arms" on the right look to me like the "arms" of many of the London livery companies, as frequently printed on their Indenture forms.
Whether they are formal arms and recognized by the Heralds, I can't say.
Now, I know that the present day arms of the Apothecaries Company are different. The questions is, what were they using back around the turn of the C18th?
I have attached the Wheelwrights' Company version, for comparison.