Nope, they are two different meanings, and it is a misunderstanding for people to consider they are the same thing. Eyesight means the ability to see objects that is natural ability when people are born with. Eye vision is described as the ability to organize, interpret and understand what you can see. For example, you could have good eyesight with poor eye vision. That is to say, you could see objects, but maybe you could not see far away or nearby objects in a clear way. You could have other eye vision problems based on you could see objects, otherwise, you are blindness.
Although it seems that people use the words "eyesight" and "vision" quite often to mean the same thing, there is the difference between them. People having perfect eyesight can still have vision problems. Eye sight is tested through one's ability to see images up close and far away. It usually means the charts with letters and numbers on them during an eye examination. At this point, the optometrist is testing for visual acuity. How accurately are your eyes seeing the image? The vision means the image that you see. The term "vision" encompasses the idea of eyesight but goes a little bit beyond it. After testing for visual acuity, eye care doctors also check to see if the eyes are working in synch, or what is called "binocularity." When two eyes are not working together, with one eye is working harder than the other, you will have experienced eye strain and headaches. If you are untreated, eyes with poor binocularity can be worse significantly.
Of course, sight is different from vision. Generally speaking, sight is the ability to interpret information and surroundings from the effects of visible light reaching the eye. We also call it as eyesight. On the other hand, vision which has the visual system, enables organisms to process visual detail, as well as some non-image forming functions. We can say that vision can interpret information from visible light to build a representation of the surrounding world. In other words, sight is the process of the eyes to focus an image on the retina; and vision is the ability of the brain to give this image meaning. Anyway, if you still have some question about them, you can just ask your eye doctor.