The Swiss Reformed theologian Bénédict Pictet (1655-1724) discusses the unity, holiness, and catholicity of the Church in his Theologia Christiana, Book XIII, Chapter III. Below is my own translation:
1. Among the attributes of the Church, the first is its unity. For since it is a sacred society comprehending all the elect, it is necessary to have some unity by which all those elect may be connected with one another; and this unity consists in those bonds which unite the members with one another.
2. Now as the Church may be considered in reference to either its external or internal state, so the bonds are of two kinds: some are internal, and others external; additionally, some bonds are essential, and others accidental.
3. The internal bonds are: (1) the unity of the Spirit (Eph. 4:3; 1 Cor. 12:13). The Spirit is the soul of the Church; by this unity of the Spirit two [or more] societies, which are animated by this same Spirit, constitute one body, even though they may be entirely unknown to one another. Thus we constitute the true body together with the churches in distant parts of the world. (2) The unity of faith (Eph. 4:4), that is, one doctrine of salvation set forth in the Gospel, which is embraced by faith. (3) The unity of love [charitatis], which follows the unity of faith, and by which the faithful who are united to Christ by faith should be gathered among themselves in love, so that the unity of the Spirit may be kept by the bonds of peace (Eph. 4:3), wherefore love is called the bond of perfection (Col. 3:14). (4) The unity of hope (Eph. 4:4); that is, of the thing hoped for and of the heavenly inheritance to which we are all equally called.
4. The external bonds are: (1) the unity of sacraments, as the unity of baptism (Eph. 4:4); and (2) the unity of ministries.
5. These are essential bonds, but there are others which are accidental, which are: (1) agreement in all dogmas; (2) unity of the form of [ecclesiastical] government; (3) unity of the same [ecclesiastical] laws; and (4) unity of the same [ecclesiastical] discipline.
6. Schism is the rupture of the bonds which constitute the unity of the Church, but schism is to be distinguished in a twofold manner: as either universal schism, by which the general truths which constitute the foundation of Christianity are renounced, or as particular schism, by which [some] truths are renounced which are of great moment, but not those general truths [which constitute the foundation of Christianity].
7. Every separation is not schism, although every schism is separation; still, every unjust separation is schism. [Note: For more on schism, see these posts by Johannes Wollebius, Heinrich von Diest, Johann Heinrich Alsted, Pierre Jurieu, and Matthew Poole]
8. The Church is called holy, (1) because God has separated it from the world to be a peculiar people (Tit. 2:14); (2) because it devotes itself to holiness, not the shadowy kind of holiness as was the holiness of the Jewish nation; and (3) because it is purified and sanctified by the Holy Spirit. It may also be called holy with respect to the doctrine which it teaches, in that the purity of its dogmas and the holiness of its precepts surpass whatever is read in legislators, hierophants, and philosophers, laudable as these may be.
9. It is called catholic, not only because of its orthodoxy, in which sense the Fathers employed the term catholic […], but (1) because it is dispersed throughout the whole world and is not affixed to a certain place, in contrast to the Old Testament Church which was confined within the narrow limits of Judea; (2) because it is read that in it there is no distinction of the race, order, or status of men, for there is no difference between Jew and Greek (Rom. 10:12; Acts 10:35); and (3) because it is bound to endure through all ages unto the consummation of the world.