The words “Unction” and “Anointing” mean exactly the same thing. Unction is simply the one borrowed directly from the Latin (unctionem, which varies depending on how it’s used in a sentence).
Extreme Unction means “anointing in an extreme situation”—in other words, when death is expected very soon. We could also say “extreme anointing” or “anointing in extremis”
The “Last Rites” (note the plural there) is a collective phrase that refers to the final rituals of the Church done for one who is very near death. The Last Rites are:
–the Sacrament of Confession (at least in the minimal form)
–the Sacrament of Communion (in this case, as Viaticum), presuming that the person is physically able to receive
–the Sacrament of Anointing (aka Sacrament of Unction)
–the Apostolic Pardon (the only one of the four that is not a Sacrament)
Not every Anointing is in extreme circumstances, so sometimes the adjective “extreme” may be added, sometimes not; therefore “extreme unction” is not always synonymous with “unction.” One may always interchange the words unction and anointing, but not always add the word extreme.
The “Last Rites” is not the same as “extreme unction” (although they are often confused). Instead, the Last Rites always includes extreme unction (as 1 of the 4). Likewise, not every anointing/unction is done within the context of the Last Rites.