Adie's tonic pupil is clinical eponym for ciliary neuropathy or ganglionopathy. Importantly, this condition produces a supersensitivity to direct cholinergic agonists via denervation effects! Weak (dilute) pilocarpine (a direct cholinergic agonist) will causes pupillary constriction in an Adie's tonic pupil because it is super sensitive to even weak pilocarpine. Whereas in other conditions, there will be no response, meaning the pupil remains dilated.
Strong (concentrated) pilocarpine will causes pupillary constriction in a 3rd nerve palsy, because it directly activates the iris sphincter muscle – it doesn't rely on CN 3.
In iris sphincter failure, such as from muscarinic antagonist (eg, atropine), the pupil will fail to constrict even with a direct cholinergic agonist. We can remember atropine's effects with the story of atropa bella donna; this plant contains atropine, and women in ancient times used it to dilate their eyes, hence bella donna for "pretty woman".