Pink eye is a lay term for conjunctivitis, like falling out (Appalachian) is a lay term for seizures. Pink eye is also used to denote a symptom of conjunctivitis. Infectious disease, allergic reactions, chemical, thermal, and traumatic injury to the eye can cause pink eye.
In an outbreak the lines can be blurred.
I worked an outbreak of mold induce conjunctivitis in which some had an actual fungal infection and others just had an allergic reaction to the mold. But they all had pink eyes.
BTW in occupational health I get to see the most inventive excuses for time away from work due to conjunctivitis and pink eye.