The difference is this:
include will not fail if it cannot find the resource, require will. Honestly, it's kind of silly that include exists at all, because if you are attempting to load a resource you are pretty much counting on it being there. If you are going to use anything, I would recommend using require_once always, that way you don't run into collisions (ie, if another script is requiring the same file) and your code always works as intended because you know the resources you are including are there (otherwise it is failing).