Do you only use "conversion by the sword" when you speak of Islam?
No. As a matter of fact, I don't. In fact, I preached at a small church for some time. I spent very, very little time talking about Muslims. I spent more time talking about Catholics and liberal protestants. I spent the most time talking about the Pharisees and Sadducees among Baptists. Biblically and historically speaking... when biblical Christians practice biblical principles and make biblical stands... God blesses.
Christianity is an inside out religion. The NT focuses on personal spiritual conversion and growth as a means for changing ourselves and the world around us. In response to a question about Christian political activism, John MacArthur once said that the best thing a Christian can do to change the country/society is to be a good witness to their neighbor and live their testimony. I would say that's pretty close to the bull's eye.
Plenty of Christians were converted through violent coercion, as well.
You and I have discussed the definition before. You bristle at my suggestion that Catholicism is not "Christian" in the biblical sense in part because of their soteriology and in part because they have a history of coercion.
Someone who becomes a Christian at the point of a sword... is not a Christian. I would submit that someone who "converts" someone at the point of the sword is not a Christian either.
Protestant, state endorsed churches have also "converted" by force. The Church of England was very abusive toward Catholics as well as dissenters such as Baptists, Separatists, Independents, et al.
Again, a plain and normative reading of the NT precludes from being "Christian" the act of forcing or coercing someone to become Christian.
So my bottom line answer is... Yes people have been converted by force by people claiming to be Christian... but No... neither party is "Christian" by the biblical definition.
It seems as though every time you mention Islam, you do so in a way in which you deride it and act as though Christianity is somehow above Islam.
Biblical Christianity when practiced is superior to Islam with regard to the treatment of non-believers, enemies, women, sinners,... It is benign with respect to civil gov't.
Christianity, Islam, Judaism, and Hinduism all have their skeletons, their hatred, and their violence to account for; none of these communities are innocent of mass atrocities against humanity.
The religion established by Jesus Christ has none of those. Men have those. Men calling themselves Christians have had and have them.
By now if nothing else, you know I am a purist. I strive for consistency in whatever it is I believe. I may well be wrong about a whole bunch of things that I have and state a strong opinion about... but at a minimum those potentially incorrect opinions are consistent with other things I believe and with the world as I am able to perceive it.
With that in mind, I reject without reservation the notion that a "real" Christ redeemed believer will use force to convert someone. It is completely antithetical to who Christ was and what He taught.