Half-and-half cannot be watered down to make milk. In a dairy context, "half-and-half" usually means an equal-parts mixture of whole milk and cream, usually used as a lower-fat alternative to cream. Cream is the high butter-fat component of milk that naturally separates from whole milk and floats on top.
If cream is removed from whole milk, the remaining milk is referred to as "skimmed" milk. While cream, whole milk and skimmed milk contain decreasing amounts of fat, adding water doesn't change one product to another, since the amount of protein and carbohydrates present get diluted as well. Adding water to cream just makes watered-down cream, and adding water to half-and-half just makes watered-down half-and-half.