In my experience, people who refer to themselves as "Christian" are evangelical or fundamentalist. Catholics say they are Catholics. Mainline Protestants say their denomination: Baptist, Episcopalian, Presbyterian, Methodist, etc. One muddying factor is that evangelical Christianity overlaps with the Mainline Protestant denominations, so some Baptists are evangelicals, as are some Presbyterians, and so on.
It has also been my experience that evangelical/fundamentalist Christians only consider those who have been born again to be true Christians. Thus, they try to convert not only Muslims, Hindus, et al., but also Catholics and Protestants who do not profess to have had a specific moment of enlightenment.
As for non-believers, non-belief for most of us is not a central part of our everyday lives, unless believers go out of their way to make life hard for us. I doubt that Christians (of all stripes) spend much time thinking about Zeus, Isis, or any of the other gods they disbelieve.