TL;DR: Linguistically, the terms Catholic Church and church catholic (alternatively Church catholic or Church Catholic) are not interchangeable.
The former refers to the theological tradition and religious institution headed by the Bishop of Rome (“the” Pope, in Western Civilization), often called the Roman Catholic Church, whereas the latter refers to the idealized concept of the body of all Christian believers.
First of all, on a purely grammatical note, the use of post-positive adjectives is well attested in English. Wikipedia provides the following handy list of set phrases with post-positive adjectives relating to Legal and general terms:
Legal and general terms: agent provocateur, battle royal, body corporate, body politic, corporation sole, cause célèbre, court-martial, fee simple, fee tail, femme fatale, force majeure, God Almighty, heir apparent, heir presumptive, knight errant, language isolate, letters close, letters patent, letters testamentary, life everlasting, the light fantastic, malice aforethought (also malice prepense), persona non grata, mens rea, pound sterling, proof positive, spaghetti bolognese, sum total, time immemorial, times past, treasure trove
This might lead us to believe that Catholic Church and church catholic/Church Catholic can be used interchangeably, where the second is merely an arcane, flowery or more literary version of the first. This is emphatically not the case.
The modern term catholic is derived from the Greek words kata and holos meaning about and (the) whole respectively. The word catholic, in theological terms means something like all embracing, universal, all encompassing and has connotations of both inclusivity and diversity.
Nowadays, however, Catholic is more commonly associated with the particular Christian church headed by the Bishop of Rome, often and especially historically also called the Roman Catholic Church (after the Roman Rite, by which Western adherents worship almost exclusively. There are Byzantine Catholics, Syriac Catholics, Chaldean Catholics, and so on, but until the modern era, few were to be found in English-speaking countries). Thus, being referred to as Catholic or a Catholic is commonly interpreted as equivalent to being a member of the [Roman] Catholic Church.
However, the idea of the catholicity of the Christian religion predates the institution of the Church of Rome. Various branches of Christianity stake equal claims to be the true expression of catholicity. Consider, per Wikipedia:
- The Eastern Orthodox Church, also known as the Orthodox Church, or officially as the Orthodox Catholic Church… teaches that it is the One, Holy, Catholic and Apostolic church established by Jesus Christ in his Great Commission… .
In addition to this, many Christians who are members of other churches also regard themselves as being part of the catholic faith in the sense of belonging to one universal overarching inclusive body of Christian believers.
This distinction between being catholic/Catholic and Catholic/Roman Catholic is brought out in the passage that the Original Poster (henceforth OP) quotes from. Here is a salient excerpt:
- One of the most frustrating difficulties encountered in discussions such as this is the fact that the starting assumptions of Roman Catholics and non-Roman Catholics are so different. (emphasis mine)
Perhaps to draw out the distinction further, take this passage by John Gargev from the book Why a Church catholic?:
Simply put my thesis is that it has never been more important than at present for Christians to be catholic. Just to state such a proposition will surely raise the hackles of many a reader, but I am convinced that it is true and thoroughly defensible. Of course, the proposition needs explanation and qualification and the first chapter attempts to provide such. For the moment, I am satisfied to set forth plainly the major contention which subsequent chapters will try to explain and establish.
One qualification needs to be made at once, however. The word "catholic" in the title is written with a small letter. It is not a proper noun, naming a particular church, but an adjective describing the church of Jesus Christ wherever it is found. Many Christians who are not Roman Catholics profess faith in the holy, catholic church according to the ancient creeds, so the Catholic Church (with capital letters) does not hold exclusive title to the name.
Now, obviously there can be a problem with using the term Catholic Church/Catholic church if a writer wants to make it clear that they are talking about the principle of an all embracing and universal church, a body of believers, even a body of churches. The reason for this is that it could easily be interpreted as referring to the specific institution which calls itself the Catholic Church, as opposed to the notion or ideal of a catholic church in principle or referring to a notional broader church (where church is perhaps best read as a body of people). Writers who wish to avoid this confusion or to make the distinction clear will often refer to the latter as the church catholic to distinguish it clearly from meaning simply the Roman Catholic Church. This distinction is not only made by writers discussing different churches, but could easily be used by Catholic writers themselves where they might argue, for example, that the the real church catholic actually is the Roman Catholic Church.
Note that for many writers the term church catholic has a similar meaning to the body politic. The term body politic is not used so much to refer to a discrete individual political body, but all the institutions and individuals involved in politics conceived of as an overarching body. Similarly the church catholic may be seen as encompassing all the individual churches and believers who are part of an overarching inclusive body of believers.
Note: I am not religious and am not a theologian. The finer points of these distinctions may well be lost on me, and I hope not to have misrepresented any of the facts here. My interest in the terminology is merely linguistic.