Unfortunately, the modern "discipleship movement" has turned discipleship into a few courses to be taken and a few boxes to be checked, with the emphasis being on teaching people how to be a "soul winner" rather than on growing in godliness. At the same time, it is equally unfortunate that the language of "discipleship" is all but absent from many of the writings of those in the confessional traditions.
At one level, to speak of being a disciple is to speak of being a Christian. After all, Acts 11:26 demonstrates that the two terms are (or at least were) synonymous. To be a disciple is to submit oneself to the teaching and discipline (way of life) of the master so as to become like the master. To be clear: the goal of "discipleship" as a concept is to become like the master in every respect, not simply to learn from the master so that their knowledge and insight can inform and even merge with your own thinking to help make you a better person. As discipleship pertains to followers of Jesus, it means that we are seeking to become like Jesus in every respect. (This is why Paul speaks of Christ being formed in us, Gal 4:19, and that we are to grow up into Christ, Eph 4:15, etc.) Thus, what we mean by the term "discipleship" is pretty much equivalent with what we mean by the term "sanctification."
Still, I actually appreciate the word "discipleship" and the focus it brings on intentionality. We are not passive in our sanctification (Phil 2:12), but all too often we approach our faith with a degree of passivity if not ambivalence - we believe (or at least claim to believe) right things, avoid doing bad things, come to church, and then go about our lives the rest of the time. Yet the concept of discipleship forces us to remember that we are followers of Christ who are seeking to learn from him, to submit our lives to his way of life, so that we can become like him. Keeping things explicit, and intentional, keeps them in focus and in mind. Things that are assumed are soon neglected and then forgotten.
A key aspect of discipleship, and therefore church life, is life together. I do think it is a shame that many Christians are content to treat church like a chapel - a place to come together to have a religious worship service with no other real interaction or involvement. We learn by observing and interacting... and by imitation. This is why so often Paul calls on his readers to imitate his example, and the example of other godly people. This is how women are to teach others to love their husbands and children, etc. The 71 verses in the NT that include the "one another" language (ie., "bear one another's burdens") speak to far far MORE than simply having an elder or the pastor pray down a sick list during the worship service. The Bible emphasizes life together, and as we teach, model, correct, challenge, serve, irritate, disappoint, forgive, restore, and help one another, and yes, as we worship alongside each other, and as we do outreach together, we operate within the matrix God has appointed for us to become like Jesus.