Actually, these are not quite homographs, since one is capitalized and the other isn’t. They are thus, rather, what I dubbed “Confusables” when introducing the feature of Confusables ® (paronym-disambiguation) into the Franklin spellers and dictionary products. Anyhow, you probably haven’t heard of either; but this one is a doozy.
(1) The better-known of these is written in all capitals: ZOG, in line with its origin as an acronym. It stands for “Zionist occupation government”; and no, it does not refer primarily to the West Bank. As to what-all it does refer to, you can easily find by googling (just be sure that you have your anti-malware software set on HIGH).
What is interesting about this is that it is among the very few terms -- and virtually unique among monosyllables -- whose mere utterance brands the utterer as a very particular political breed of beast.
These are harder to find than you’d think. The only one that springs immediately to mind is “Social-Fascist” (and its German equivalent), whose use invariably revealed the user as a Third Period Stalinist (or at least someone parotting their patter). The use of the term liberal as a sneer-word (as opposed to simply denouncing concretely various policies of liberals) does tell the listener quite a bit about the user, but of course the word is used objectively as well. The term reactionary is almost always a sneer-word for conservative (thus revealing much about the speaker), but it can also be used, cavalierly, as a defiant synonym of laudator temporis acti (indeed, the historian John Lukacs self-applies the label). The concept Antichrist makes sense only in a Christian context, but you can easily discuss the term (say, in comparing it to that of the Dajjâl ) without subscribing to any of the tenets of that belief-system. ZOG is different.
It’s not just that most people don’t believe a “Zionist occupation government” (in the intended sense) exists. After all, people use terms like Santa Claus, unicorn, phlogiston, Higgs boson, and will even predicate positive qualities of them (“Santa wears a red suit”, “the Higgs boson is necessary for the consistency of the Standard Theory”) without thereby making any existential commitment (Quine’s term) at all.
(2) As a (somewhat nonce) term in physics, it is written in lower-case. Here is the first (and only) passage in which I encountered the term:
Massive particles of spin 1 can be described as having three ingredients: a left-handed zig (helicity 1), a right-handed zag (helicity -1), and a non-spinning ‘zog’ (helicity 0).
-- Roger Penrose, The Road to Reality (2004), p. 653