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The word “schism” is any division; it isn’t a Catholic-only term.

Well, let's check on that:

Schism:

A willful separation from the unity of the Christian Church. Although St. Paul used the term to condemn the factions at Corinth, these were not properly schismatical, but petty cliques that favored one or another Apostle. A generation later Clement I reprobated the first authentic schism of which there is record. Paul's exhortation to the Corinthians also gives an accurate description of the concept. "Why do we wrench and tear apart the members of Christ," he asks, "and revolt against our own bodyk and reach such folly as to forget that we are members of one another?" While the early Church was often plagued with heresy and schism, the exact relation between the two divisive elements was not clarified until later in the patristic age. "By false doctrines concerning God," declared St. Augustine, "heretics wound the faith; by sinful dissensions schismatics deviate from fraternal charity, although they believe what we believe." Heresy, therefore, by its nature refers to the mind and is opposed to religious belief, whereas schism is fundamentally volitional and offends against the union of Christian charity. (Etym. Latin schisma; from Greek skhisma, a split, division, from skhizein, to tear, rend.)

From the Modern Catholic Dictionary

Schism (from the Greek schisma, rent, division) is, in the language of theology and canon law, the rupture of ecclesiastical union and unity, i.e. either the act by which one of the faithful severs as far as in him lies the ties which bind him to the social organization of the Church and make him a member of the mystical body of Christ, or the state of dissociation or separation which is the result of that act. In this etymological and full meaning the term occurs in the books of the New Testament. By this name St. Paul characterizes and condemns the parties formed in the community of Corinth (1 Corinthians 1:12): "I beseech you, brethren", he writes, ". . . that there be no schisms among you; but that you be perfect in the same mind, and in the same judgment" (ibid., i, 10). The union of the faithful, he says elsewhere, should manifest itself in mutual understanding and convergent action similar to the harmonious co-operation of our members which God hath tempered "that there might be no schism in the body" (1 Corinthians 12:25). Thus understood, schism is a genus which embraces two distinct species: heretical or mixed schism and schism pure and simple. The first has its source in heresy or joined with it, the second, which most theologians designate absolutely as schism, is the rupture of the bond of subordination without an accompanying persistent error, directly opposed to a definite dogma. This distinction was drawn by St. Jerome and St. Augustine. "Between heresy and schism", explains St. Jerome, "there is this difference, that heresy perverts dogma, while schism, by rebellion against the bishop, separates from the Church. Nevertheless there is no schism which does not trump up a heresy to justify its departure from the Church (In Ep. ad Tit., iii, 10). And St. Augustine: "By false doctrines concerning God heretics wound faith, by iniquitous dissensions schismatics deviate from fraternal charity, although they believe what we believe" (On Faith and the Creed 9). But as St. Jerome remarks, practically and historically, heresy and schism nearly always go hand in hand; schism leads almost invariably to denial of the papal primacy.

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. On the other hand, schism does not necessarily imply adhesion, either public or private, to a dissenting group or a distinct sect, much less the creation of such a group. Anyone becomes a schismatic who, though desiring to remain a Christian, rebels against legitimate authority, without going as far as the rejection of Christianity as a whole, which constitutes the crime of apostasy.

Formerly a man was rightly considered a schismatic when he disregarded the authority of his own bishop; hence the words of St. Jerome quoted above. Before him St. Cyprian had said: "It must be understood that the bishop is in the Church and the Church in the bishop and he is not in the Church who is not with the bishop" (Epist., lxvi, 8). Long before, St. Ignatius of Antioch laid down this principle: "Where the bishop is there is the community, even as where Christ is there is the Catholic Church" (Smyrnæans 8.2). Now through the centralizing evolution which emphasizes the preponderant rôle of the sovereign pontiff in the constitution of ecclesiastical unity, the mere fact of rebelling against the bishop of the diocese is often a step toward schism; it is not a schism in him who remains, or claims to remain, subject to the Holy See. In the material sense of the word there is schism, that is rupture of the social body, if there exist two or more claimants of the papacy, each of whom has on his side certain appearances of right and consequently more or less numerous partisans. But under these circumstances good faith may, at least for a time, prevent a formal schism; this begins when the legitimacy of one of the pontiffs becomes so evident as to render adhesion to a rival inexcusable. Schism is regarded by the Church as a most serious fault, and is punished with the penalties inflicted on heresy, because heresy usually accompanies it. These are: excommunication incurred ipso facto and reserved to the sovereign pontiff (cf. "Apostolicæ Sedis", I, 3); this is followed by the loss of all ordinary jurisdiction and incapacity to receive any ecclesiastical benefices or dignities whatsoever. To communicate in sacris with schismatics, e.g., to receive the sacraments at the hands of their ministers, to assist at Divine Offices in their temples, is strictly forbidden to the faithful.

Some theologians distinguish "active" from "passive" schism. By the former they understand detaching oneself deliberately from the body of the Church, freely renouncing the right to form a part of it. They call passive schism the condition of those whom the Church herself rejects from her bosom by excommunication, inasmuch as they undergo this separation whether they will or no, having deserved it. Hence, this article will deal directly only with active schism, which is schism properly so-called. It is nevertheless clear that so-called passive schism not only does not exclude the other, but often supposes it in fact and theory. From this point of view it is impossible to understand the attitude of Protestants who claim to hold the Church they abandoned responsible for their separation. It is proved by all the historical monuments and especially by the writings of Luther and Calvin that, prior to the anathema pronounced against them at the Council of Trent, the leaders of the Reformation had proclaimed and repeated that the Roman Church was "the Babylon of the Apocalypse, the synagogue of Satan, the society of Antichrist"; that they must therefore depart from it and that they did so in order to re-enter the way of salvation. And in this they suited the action to the word. Thus the schism was well consummated by them before it was solemnly established by the authority which they rejected and transformed by that authority into a just penal sanction.

From the 1910 Catholic Encyclopedia

SCHISM: A term generally applied to the division that, either wholly or partly, suspends the outward unity of the Church; also, in Roman Catholic canon law, the offense of producing or attempting to produce such a division, and further, the deliberate withdrawal from the bond of the Church by a refusal of obedience to its authorities Nature on the ground that their powers are and not legitimate. But mere insubordinaClassifica- tion to particular rulings or commands tion. of the authorities and simple resistance do not constitute schism. Where secession ensues from denying individual confessional doctrines of the Church, that is, where the offense of schism is concurrent with heresy, it is termed "heretical schism." On the other hand, in the case of separation, when, for instance, the papacy is acknowledged per se but the actual pope is declared not legally elected, the schism is named "pure schism." A further distinction is drawn between "particular" and "universal" schism, according as unity with the whole Church is ruptured directly, as by secession from the pope; or only indirectly, by separation from another ecclesiastical superior, particularly from the bishop. According to Roman Catholic canon law, schism constitutes an ecclesiastical offense chargeable before the spiritual tribunal, and is threatened with summary excommunication, forfeiture of office, suspension from holy orders, disqualification for church positions, infamy, and confiscation of property.

From the New Schaff-Herzog Encyclopedia of Religious Knowledge (a thoroughly Protestant source)

So, in other words, if a particular congregation decided to have a friendly division into multiple parts (say because it was getting too big), that would not be considered (in a theological sense) a schism. Likewise, if a particular Church was granted autocephality, that would not be considered a schism (at least in a theological sense). A schism, while it might be polite, involves a break in communion, whatever the scope.