This issue was mentioned in the answer to this question, but I don't see any further discussion.
Terms used so far include:
I have a slight preference toweards bitcoin.org client, as it's very clear which one is meant by it.
Also, is capitalisation important?
I personally refer to it as "standard client", but I don't see anything wrong with having a couple synonyms.
As for capitalization, it really depends - whether we use it as a name of the client, or as a description of it. In my master thesis I was capitalizing all Bitcoin-related terminology (like Address, Transaction, Network, etc), which made things quite easy to distinguish from non-Bitconi terminology. However, it would be hard to encourage most users to do the same.
We've actually had the capitalization question before, so I'll let that answer stand on its own. As for the name of the application, I'm fond of "Satoshi Client" but really any of the options specified do an adequate job of correctly identifying the appropriate client. If you're asking about tags, on the other hand, we've had a standard-client tag for quite some time (68 questions using it at the time of this writing) so that is our preferred terminology here, at least for the purpose of tagging.
