The answer is in your question:
The alias registers have different addresses compared to the original register for which they are aliased.
That is exactly what an alias is; literally a different name for the same thing. Specifically in this case a different address to the same physical register.
It is usually an artefact of incomplete address decoding. If you have an I/O space of say 256 registers, you only need 8 address lines, but if your address bus is 16 bits for example, it is simpler to leave the higher address lines unconnected that to explicitly decode them, so the I/O space repeats every 256 bytes (in this example). Otherwise you would have to OR the high order address lines together with the /CS line to avoid the aliasing to no particular benefit.