An Artifact is an object made by a human being, typically an item of cultural or historical interest. Where as a Relic is simply a an object surviving from an earlier time, especially one of historical or sentimental interest. So my view is a Artifact is more historical or from the cultural past and a Relic is something more mundane and more of a personal nature.
As far as locations early in the game, I would think both would be located scattered around the world in places not typically accessed. As the game progresses you probably can find some in stores, local auctions, or from an individual.
As far as Effects, no one really knows yet. I would think some would have some effects and some will not. Just remember that the effects can be positive or negative so finding one may not always be directly beneficial. Or if it is it may have a negative side to consider as well.