To the liberal, these words have no meaning because, after all, Jews and Muslims and Protestants and practitioners of Voodoo all belong to the one true church, all have covenants with God, and all are saved.
To the conservative Catholic, "schismatic" is used to label those Catholics who worship in the same way that all Catholic worshipped and who believe the same way that all Catholics believed for 1,965 years. In order to be logically consistent, they'd have to accuse Pope St. Pius IX of "schism" with his "Syllabus." Pope Pius XI's "Quas Primas" and Pope Leo XIII's "Testem Benevolentiae Nostrae" would have to be considered expressions of "schism" because they deny the neo-Catholics' Americanist views. God forbid they should read Pope Gregory XVI's "Mirari Vos" and consider the ridiculousness of the Vatican II experiment. Why, anything short of idolizing the Pope is "schism," of course. Conservatives are often seen hurling Canon 751 of the 1983 Code of Canon Law at traditionalists, like Protestants using Ephesians 2:8-9 as a weapon against the Catholic's stress on the importance of works, entirely forgetting James 2:24. Canon 751 reads:
Heresy is the obstinate denial or doubt, after baptism, of a truth which must be believed by divine and catholic faith. Apostasy is the total repudiation of the Christian faith. Schism is the withdrawal of submission to the Supreme Pontiff or from communion with the members of the Church subject to him.
They won't tell you about Canon 1323, which reads:
No one is liable to a penalty who, when violating a law or precept:
1° has not completed the sixteenth year of age;
2° was, without fault, ignorant of violating the law or precept; inadvertence and error are equivalent to ignorance
3° acted under physical force, or under the impetus of a chance occurrence which the person could not foresee or if foreseen could not avoid;
4° acted under the compulsion of grave fear, even if only relative, or by reason of necessity or grave inconvenience, unless, however, the act is intrinsically evil or tends to be harmful to souls;
5° acted, within the limits of due moderation, in lawful self-defense or defense of another against an unjust aggressor;
6° lacked the use of reason, without prejudice to the provisions of canon. 1324, §1, n. 2 and 1325;
7° thought, through no personal fault, that some one of the circumstances existed which are mentioned in nn. 4 or 5.
Yes, in the real world, schism is the obstinate refusal to be subject to the Pope, a denial of his right to rule. It is not disobedience, which sometimes we must engage in, as did St. Athanasius (kicked out of his Bishopric, exiled, adamant against the sinful hierarchs, excommunicated by Pope Liberius, but later canonized) if what we are ordered to do by legitimate authority harms the faith (see Aquinas's Summa Theologica II-II-104).
Even the Catholic Encyclopedia (1917) has it figured out:
Schism, therefore, is usually mixed, in which case, considered from a moral standpoint, its perversity is chiefly due to the heresy which forms part of it. In its other aspect and as being purely schism it is contrary to charity and obedience; to the former, because it severs the ties of fraternal charity, to the latter, because the schismatic rebels against the Divinely constituted hierarchy. However, not every disobedience is a schism; in order to possess this character it must include besides the transgression of the commands of superiors, denial of their Divine right to command.
In case you haven't heard before, let me be the first to inform you: traditional Catholics do not deny the Divine right of Catholic hierarchs to command. We do believe, however, that they have no "Divine right" to command sin, to transgress eternal law, to attempt to change the deposit of the faith, to harm souls, to lead souls to Hell, to water down doctrine, etc. Given the state of our parishes, traditional priests and lay Catholics are justified in their actions. Per Canon 1323, we believe that it is a "grave inconvenience" to be forced to attend Protestantized Masses and hear priests water down our Faith with liberalism. We have a "grave fear" that compels us to carry on in the traditional way in order to preserve the Faith and save souls. We do this by "reason of necessity." Ergo, no schism. In addition to this fact, it is traditional Catholics who decry the new "collegiality" that weakens the papacy! But it's the neo-conservative Catholics who ignore the Nota Praevia to Lumen Gentium, the liberals who hate the very idea of the papacy, and the recent Popes themselves who behave as though they don't accept traditional Catholic doctrine as they go about kissing the rings of Anglican "Bishops" and such. We "deny the Pope's Divine right to rule?" Ha! We wish they would rule!