What's the difference between pink eye and herpes viral infection of the eye? Can you get either one from herpes simplex on the lips?

Different virus. Although the term "pink eye" is somewhat vague, it typically refers to an infection caused by adenovirus, is quite common, and highly contagious. Herpes simplex is also a virus which can cause an eye infection, is much less common, and can potentially be much more serious. You will need to see your eye md to distinguish the two.
Bad luck or hygiene. Most "pink eye" is caused by a viral infection on the inner part of the eyelid and thin moist "skin"covering the eyeball-called the conjunctiva. Infection occurs when you touch a surface (or person) with the virus and rub your eye-transfering the virus. Frequent hand washing helps prevent this. Sharing towels or pillows can also cause infection. Herpes infection is directly person to person.