Douglas Summers,
I guess you mean the Church when you refer to Christianity?
I mean Christianity when I refer to the Church.
Each denomination of Christianity thinks it's "the Church". Acknowledged outright (e.g., RCC) or covertly by a continued separate existence. Each denomination equates its own interpretation of "the Church" with that which is described in the Bible. Christianity misses the mark because inevitably Christian Biblical interpretations boil down to the perpetuation of denominational thinking.
Christians not only interpret what the Bible means (a myriad of commentaries), they interpret what the Bible says by interpretive translation (a myriad of English translations). Even the most literal of English translations aren't entirely literal. Wherever interpretive translation is found, it isn't a literal translation. There are several instances where translations translate according to a Tradition. The JW's aren't the only ones guilty of translating the Bible interpretively to make it agree with their own Tradition. The following is a case in point.
In the KJV and in most modern translations, the NT Greek word "ekklesia" is translated by the English word "church". The two words are NOT equivalent.
The English word "Church" has as its root the Greek word "kyrios" meaning "lord". It was originally used to refer to "the Lord's house". The word became more inclusive with time. Both the Oxford and Mirriam-Webster dictionaries refer to the root and developmental history of the English word in their definitions.
The Greek word "ekklesia" has as its roots two Greek words, "ek" meaning "out of" and "kaleo" meaning "to call". Thus the literal meaning of the word "that which is called out of".
Ekklesia was originally a secular term that referred to a group of people called out of a city population to take care of the affairs of the city. Much like a City Council today. I don't remember the source for the term's secular use. I only remember reading about it a few years back in more than one source. Secondarily it refers to any association of people that are called out of a population for a certain purpose (Acts 7:38, a reference to the Jews called out of Egypt by God, and by extension out of the world for his purpose; Acts 19:32, 39, 41 -- where in the KJV and most modern translations, the word assembly translates the same Greek word usually translated as church, since it obviously isn't a reference to a those who are in Christ).
The NT writers, when referring to the gathering of those who are in Christ, use the word ekklesia in basically the same way as the secular usage. People within a city being called out by God in Christ through the Spirit to take care of his own affairs in that city. It's a necessary variation of the OT economy in Israel wherein one city, Jerusalem, was the center of gathering. Because the Tabernacle/Temple was in Jerusalem. It's the OT economy that Christianity imitates with their universal Church institutions. Since the new economy includes both Jew and Gentile believers, the center of gathering changed. The new center of gathering became individual cities wherein those in Christ reside.
Each ekklesia is autonomous, named for the city in which it exists (e.g., Rev 1:11). Each with his Son as head (Eph, Col, Rev). When more than one ekklesia is referred to, ekklesia is plural (Acts 9:31; Rom 16:16; 1 Cor 16:19; 2 Cor 8:1; Gal 1;2, 22). There's no such thing as a universal Church (i.e, the Church) in the NT. Only local ekklesia.
In Ephesians, the context is that of a local ekklesia (Eph 1:1). Each ekklesia (specifically in this context of the one in Ephesus) is intended to be expressions of that which is universal. The body of Christ of which he is the head (Eph 1:19-23, 4:5; see with reference to the ekklesia in Corinth - 1 Cor 12:12-26). The temple or residence of God through the Spirit (Eph 2:18-22; see with reference to the ekklesia in Corinth - 1 Cor 3:16-17). The kingdom of the Son of which he is Lord (Eph 3:5-13; see also Col 1:13 & 2 Pet 1:5-11).
In Catholicism, "the Church" on earth is only universal (i.e., world wide.). Locality is usually defined as a parish in subjection to the whole. When Catholics say they're going to Church, it's a reference to more than just a local congregation. The universal Church according to Catholicism is visible in part and invisible in part. That which is on earth is fully visible in its universality.
Key verses the RCC uses as a foundation for its own claim to be "the Church" are Matt 16:13-20 and 18:15-20. Which they have interpreted to refer to a universal Church. Universal even historically. These verses are in actuality a reference to the ekklesia in Jerusalem and was a prophecy about Peter in relation to that ekkesia. A prophecy that was clearly fulfilled as recorded in Acts 1-15. There is also the obvious implication of the keys given to Peter that must of necessity be passed on, according to the RCC, if ekklesia in Matt 16 & 18 refer to universality instead of locality.
In Protestantism, the "Church" is generally defined as two-fold. As having two aspects -- Universal and local. In its universality it's invisible. In its locality it's visible.
Protestantism, being more like the RCC than they care to admit, having perpetuated the idea of a universal Church; must of necessity interpret Matt 16 & 18 in such a way so as to not affect their own idea of the Church as referring to themselves. While simultaneously giving no ground to the interpretation of the RCC. Thus they emphasize the rock as having to do with anything except that to which it refers. Not considering Peter's eventual function in the ekklesia in Jerusalem. A function for which Peter was specially chosen by the Son. Because the Ekklesia in Jerusalem would be the pattern for all ekklesia to come (Acts 2:42-47).
So in answer to your question, we no doubt think of different things when "the Church" and Christianity is mentioned. When I refer to Christianity, I'm thinking of the man-made religion that is composed of denominations that it calls Churches. In contradiction to the desire of the one who is supposedly their Lord (John 17:17-23). When I refer to Churches or what to me is the mythical idea of "the Church", I'm not thinking of anything that has to do with the Biblical kingdoms of God or of his Son. Only to the denominations of Christianity and their local expressions that they call "churches".