This is inevitable since the size of the domain is greatly larger than the size of the target. So the chances that two different inputs would produce the same hash is greater than zero. However, as you correctly noted, the chances are so small, that practically they are considered to be zero.
I get it. This cannot be 1-to-1 mapping. It has to be many-to-1 mapping due to fact that the size of the first domain, by definition, is much larger than the size of second domain.