basicly, it works like this:
Christians include all denominations, including catholicism, eastern orthodox, etc. Therefore, catholics are a 'type' of christian. It functions similar to vegan and vegetarian. vegans are a type of vegetarian, but not all vegetarians are vegan. There are philosophical differences within and between these groups too--reaching a broad spectrum of beliefs and practices.
The 'first' church was the "catholic church" which divided into the roman catholic and eastern orthodox churches after the councel of nicea when there was a theological debate between the use of the term 'filioque' in the nicean creed. "filioque" means "and the Son" and was part of the trinity document. There was confusion about the use of this term, which started the debates. And then, this lead to the primary theological difference between these two groups: resurrection theology (roman catholic) and incarnation theology (eastern orthodox).
The next big split was the reformation (Lutherans), and of course then the formation of the Anglican Church (also called episcopal). These were both responses to roman catholicism. Therefore, these are protestants of roman catholic doctrines. And then there are various strains of anabaptists, calvinists, and various other strains such as puritains who spawned groups like shakers. Many protestant churches in the US today are actually uniquely american, developing after certain groups from these variousstrains (anabaptist, calvin--particularly) came to the US and formed other churches. Some churches are 20th century denominations; some of them were formed within the last 10 years even.
What is interesting is not just the changes in doctrine, but also the changes in perspectives and teachings regarding other churches. Catholics are often maligned because they 'use a different bible' but this isn't 'really' the case. The first offically canonized text was the catholic canon decided at the council of carthage in the 400s. this included the OT texts plus the dueterocanonical texts and the NT as it is today. There were coplies in latin, used in masses, and copies in vulgar (local) languages to be used at public readings. So, there's this 'myth' that the bible wasn't accessable to the 'average person' which is untrue, as there were public readings.
In the 1600s, the king james translation was commissioned. some important things happened between this translation and the original canonization (there were canoniztaions prior, but they were regional--maronite and ethiopean canons). First, after the catholic canon was made, the jewish community noticed that deutero canonical texts (that is, texts written by diasporic hebrews or local hebrews in the judean region in greek) were included, so they decided to make their own canon--which is basicly the same except they remove the dueterocanonicals. Then, you have luther--who believed that certain books should be removed. not necessarily the duetero canonical texts, but others such as Jude. Around this time, you also have the advent of the printing press, which ushers a way to a largely literate population. And finally, you have the 'break' with the catholic church into the anglican church.
So, James wanted a translation. Erasmus, the translator, decided to defer to the jewish canon, but still wanted to include the deuterocanonical texts because of their importance to christianity (and the anglican church wasn't a far cry from catholicism theologically or traditionally anyway). Part of the reason for an english translation was the same reason as the latin translation--so there was a common text used for masses, etc--which may have been the origin of masses/services in the local languages. So, the dueterocanonical texts were included in the "king james version" at the end of the texts. So, the organization was like this: Jewish canon, deuterocanonicals, and new testimant canon.
Of course, printing was now a common practice--for the most part--which means that you have what we have today--multiple printings, right? First editions, second editions, etc. These editions are often changed for grammatical errors or translation errors or simply for translation ideas that change. Over the years, there were many editions of the King James version printed--and restructured, including one that had the texts in this order: jewish canon, new testament, and deuterocanonical texts.
Then, the americans get into the act. The first versions of the bible in the US were two kinds: catholic canon in it's order in latin and local language versions (ie, spanish, french, noteably, and a few english once those catholics started coming over). But, most english speaking people used the king james version, and most christians who were english speaking were protestants of either anglicanism or of catholicism. Of course, there were others who came as well--such as the various groups from germany and scandenavia and other parts of northern europe, where lutheranism and various anabapist traditions had a strong foothold. They generally carried the catholic canons (there was a lutheran canon as well, early on, that was later cast aside)--which was in their languages. So, you have a number of bibles floating around--most noteably catholic in various languages and the king james version in it's more modern order of jewish texts, new testament, and dueterocanonical texts.
Then, something changed in the 1800s, which was part of the huge advent of anticatholicism in the US--the idea that catholics have a different, and therefore fallacious, bible--The New Jerusalem printing of the King James Version. THis version was printed in the US for a US market. This printing contained only the jewish canon and the new testament, no deuterocanonicals. This is when the dueterocanonical texts were given the term "apocrypha" or "apocryphal" which means 'false or errant." in truth, the catholic church considers very few non-canonical texts 'apocrypha' or 'apocryphal' and regional churches (such as armenian, byzantine, coptic, etc--which are considered 'in union with rome, though culturally distinctive') were allowed to use their cultural traditions and gospels, as well as the teachings of their founders, as elements of gospel revelation to that church in that time and place. So, it was quite an affront to many to call those books "apocryphal."
since that publishing in the 1800s, there are two bibles sold in the US: protestant canons and catholic canons. There are multiple translations of course including the new international version (NIV), the New King James (modernized the language), the New American version, and a myriad of others including one that is called the 'modern language' bible which is a horrifyingly bad translation. Yet, people still use it.
So, part of the reason why people make the distinction is that sometimes it is important. If we go to the veggieboards gathering, we'd probably like to know which are vegan and which are vegatarian as we open a dialogue or search for a restaurant or whatever. When christians open a dialogue, or a nonchristian opens one about a christian topic or such, it may be helpful to say which demonination or theological perspective one is coming from.
catholicism is different, but the differences are relatively minimal. And they are a christian denomination.