Objection 1. It would seem that the ceremonies of the Old Law are unsuitably divided into "sacrifices, sacred things, sacraments, and observances." For the ceremonies of the Old Law foreshadowed Christ. But this was done only by the sacrifices, which foreshadowed the sacrifice in which Christ "delivered Himself an oblation and a sacrifice to God" (Ephesians 5:2). Therefore none but the sacrifices were ceremonies.
Objection 2. Further, the Old Law was ordained to the New. But in the New Law the sacrifice is the Sacrament of the Altar. Therefore in the Old Law there should be no distinction between "sacrifices" and "sacraments."
Objection 3. Further, a "sacred thing" is something dedicated to God: in which sense the tabernacle and its vessels were said to be consecrated. But all the ceremonial precepts were ordained to the worship of God, as stated above (Article 1). Therefore all ceremonies were sacred things. Therefore "sacred things" should not be taken as a part of the ceremonies.
Objection 4. Further, "observances" are so called from having to be observed. But all the precepts of the Law had to be observed: for it is written (Deuteronomy 8:11): "Observe [Douay: 'Take heed'] and beware lest at any time thou forget the Lord thy God, and neglect His commandments and judgments and ceremonies." Therefore the "observances" should not be considered as a part of the ceremonies.
Objection 5. Further, the solemn festivals are reckoned as part of the ceremonial: since they were a shadow of things to come (Colossians 2:16-17): and the same may be said of the oblations and gifts, as appears from the words of the Apostle (Hebrews 9:9): and yet these do not seem to be inclined in any of those mentioned above. Therefore the above division of ceremonies is unsuitable.
On the contrary, In the Old Law each of the above is called a ceremony. For the sacrifices are called ceremonies (Numbers 15:24): "They shall offer a calf... and the sacrifices and libations thereof, as the ceremonies require." Of the sacrament of Order it is written (Leviticus 7:35): "This is the anointing of Aaron and his sons in the ceremonies." Of sacred things also it is written (Exodus 38:21): "These are the instruments of the tabernacle of the testimony... in the ceremonies of the Levites." And again of the observances it is written (1 Kings 9:6): "If you... shall turn away from following Me, and will not observe [Douay: 'keep'] My... ceremonies which I have set before you."
I answer that, As stated above (1,2), the ceremonial precepts are ordained to the Divine worship. Now in this worship we may consider the worship itself, the worshippers, and the instruments of worship. The worship consists specially in "sacrifices," which are offered up in honor of God. The instruments of worship refer to the "sacred things," such as the tabernacle, the vessels and so forth. With regard to the worshippers two points may be considered. The first point is their preparation for Divine worship, which is effected by a sort of consecration either of the people or of the ministers; and to this the "sacraments" refer. The second point is their particular mode of life, whereby they are distinguished from those who do not worship God: and to this pertain the "observances," for instance, in matters of food, clothing, and so forth.
Reply to Objection 1. It was necessary for the sacrifices to be offered both in some certain place and by some certain men: and all this pertained to the worship of God. Wherefore just as their sacrifices signified Christ the victim, so too their sacraments and sacred things of the New Law; while their observances foreshadowed the mode of life of the people under the New Law: all of which things pertain to Christ.
Reply to Objection 2. The sacrifice of the New Law, viz. the Eucharist, contains Christ Himself, the Author of our Sanctification: for He sanctified "the people by His own blood" (Hebrews 13:12). Hence this Sacrifice is also a sacrament. But the sacrifices of the Old Law did not contain Christ, but foreshadowed Him; hence they are not called sacraments. In order to signify this there were certain sacraments apart from the sacrifices of the Old Law, which sacraments were figures of the sanctification to come. Nevertheless to certain consecrations certain sacrifices were united.
Reply to Objection 3. The sacrifices and sacraments were of course sacred things. But certain things were sacred, through being dedicated to the Divine worship, and yet were not sacrifices or sacraments: wherefore they retained the common designation of sacred things.
Reply to Objection 4. Those things which pertained to the mode of life of the people who worshipped God, retained the common designation of observances, in so far as they fell short of the above. For they were not called sacred things, because they had no immediate connection with the worship of God, such as the tabernacle and its vessels had. But by a sort of consequence they were matters of ceremony, in so far as they affected the fitness of the people who worshipped God.
Reply to Objection 5. Just as the sacrifices were offered in a fixed place, so were they offered at fixed times: for which reason the solemn festivals seem to be reckoned among the sacred things. The oblations and gifts are counted together with the sacrifices; hence the Apostle says (Hebrews 5:1): "Every high-priest taken from among men, is ordained for men in things that appertain to God, that he may offer up gifts and sacrifices."
Source: Summa Theologica (New Advent)