You can get a better understanding of what something is, by being aware of what it is not. To better understand what the church is, let's consider what it is not.
The idea of being inter-denominational is that division in the body of Christ is tolerated. Each denomination keeps its distinctive name, creed, and practice. But it takes a neighbourly view of other denominations. It won't break down its walls, but it will reach over its walls and shake hands. Paul commanded that "there be no divisions among you, and that you be perfectly united in mind and thought"(1Co 1:10-13). The church of Christ assumes that this command applies not only to unity within the local church, but right across the Christian brotherhood. The inter-denominational way is a compromise that falls short of proper unity. We need to be un-denominational—doing awaywith denominationalism altogether.
The church of Christ is not “a new denomination”
To be a new denomination, we would have to be different to what has gone before, and there would have to have been a recent inauguration of the first congregation of our kind. But churches like ours have always been in existence since the inauguration of the first church of Christ in Jerusalem circa AD33(Acts 2). The church of Christ is clearly not a new denomination. It is not even the oldest denomination, because it started before any Christian denomination whatsoever came into being.
God's word is a "seed... imperishable... living and enduring"(1Pe 1:23). Plant that seed in people's hearts today, and if the heart is good soil (Lke 8:4-8) it will produce the same kind of Christian, and the same kind of church, as it did in the first place in Jerusalem circa AD33. God's word still reproduces after its kind. It does not produce denominations. It produces the same church that existed before any denominations came into being.
The church of Christ is not “an alternative church”
Many churches today are being established outside of the “mainstream denominations” as a reaction to the establishment. It is attractive to some people to break with tradition. The church of Christ however follows and adheres to the oldest Christian tradition of all: the original teaching of the church in the time of Christ and his apostles. We believe there is no alternative. Only the original gospel will do (Rom 1:16).
The church of Christ is not “a sect”.
The term “sect” now applies to churches which abuse their members with tyrannical rules and restrictions. Such churches take control of people's minds, bodies, possessions, money, time, relationships, and so forth. A sect intrudes into the privacy of people's lives and sets up a guilt-driven regimen which its members must follow or be punished. A sect practices “shunning” and various forms of harassment upon people who try to leave and go their own way. The church of Christ does none of these things. It leaves people free to run their own lives, and to make their own application of God's word, for which they are personally accountable to God. Those who set their hearts on doing that, will find a warm welcome and gentle shepherding, which they accept without duress. At all times they give and receive entirely by the exercise of their own free will. The making of rules and laws is discouraged in the church of Christ (1Jn 5:3). The law of Jesus Christ, and nothing more, is the only burden laid on members of his church.