A Traditional Catholic in the Roman Rite is a Catholic who attends the Traditional Mass exclusively, or makes every possible effort to do so.
A Traditional Catholic priest in the Roman Rite is one whose only sources of Divine worship are the Traditional prayer books of the Latin Church: the Roman Breviary, and, for the Mass, the Traditional Roman Missal. More often than not, he attended a Traditional Catholic seminary, where he was formed, both liturgically and doctrinally, in the Traditions of the Latin Church.
Why is this important? Because identity is important. We are what we are, we believe and act as Latin Catholics before the Council always believed and acted. We have suffered a lot to defend our position, our views, and the way we pray and worship, and we are prepared to do so because we believe it is the best option for Divine worship, and the most surely proven path to a saintly life, as the lives of centuries of saints made clear.
Traditional Catholic priests and laity have caused, and will cause, scandal -- they are merely fallen human beings. We have our own share of misfits, God knows well...
But, please, do not impute to us the failings of others, including priests whose whole lives and formation were undertaken in the Novus Ordo, according to the practices of liberal seminaries of a post-Conciliar style. To each his own: that is a simple matter of justice.