Calling Load(AssemblyName) is not necessarily the same as calling Load(String). If the AssemblyName.CodeBase is not set, then they do do the same thing. So, if you've set the AssemblyName.Name, CultureInfo, public key token / public key and/or Version properties, it would be the same as if you had specified those properties in a String (as a display name) and passed that to Load(String).
If the CodeBase is set, but the Name is not, however, then it's the same as calling Assembly.LoadFrom() on that CodeBase.
When both the CodeBase and the Name are set, then the bind is tried with all the given binding information except the CodeBase (so, again, just like calling Load(String)). If that succeeds, we're done. But, if that fails, then the bind is tried again with just the CodeBase (just like LoadFrom()). If it fails again, then, of course, the whole bind fails. But, if it succeeds, then we verify that the binding properties in the AssemblyName match the found assembly. If they don't match, a FileLoadException will be thrown for hresult FUSION_E_REF_DEF_MISMATCH.
So, setting both the CodeBase and the Name is useful for when you want to both load an assembly at a given path into the LoadFrom context, and verify that it has the public key token, etc. that you expect. Of course, as described above (and due to binding context rules), keep in mind that just because you call Load(AssemblyName) with a CodeBase, it does not mean that it will be loaded from that path.