Hello, a blocked tear duct means that something is stopping the flow of tears away from the eye down the tear duct into the nose. If you get blocked tear duct, your one or both eyes maybe affected. However, stye are lumps in or along the edge of an eyelid. It may be painful or annoying, but they are usually not serious. Usually it can go away naturally without some treatment.
Well, it seems that you know little about these problems with eyes. And as a matter of fact, both of them could be quite serious and give rise to some consequences if they are not cured in time. So, generally speaking, stye happens around your eyelid and eyelash, which could lead to swelling eyes and red eyes, with painful feelings, and blocked tear duct could make your eyes keep watery non-stop. Anyway, try to consult a doctor if anything goes wrong.