Matins (morning prayer), Vespers (evening prayer), and Compline (night prayer) are the 3 sections of the Divine Office that are commonly used in Byzantine Churches (Catholic and Orthodox) for public worship.
Evening Divine Liturgies are usually (but not always) preceeded by Vespers.
Morning Liturgies are usually preceeded by Matins.
Compline is often done as a stand-alone, but I have seen vespers followed by a class and closed with Compline.
The terms used are Latin, which said, since latin is the language of the Catholic Church as a union, are universal terms.
Orthros is the Greek term for Matins.
There are 8 prayers in the daily cycle of the divine office… about every 3 hours… and the long ones take about 30 minutes, while the short ones can be done in 10minutes as a group.
Deacons, priests, and bishops are required to say the divine office every day, either in the form of the 8 prayers, or in a condensed form (usually used as an Oikonomia for married or civilly employed) involving morning, mid-day, and evening prayers. This requirement is bound upon all the Catholic ordained clerics (Deacons, Priests and Bishops) and upon lesser clerics if their bishop imposes it. Monastics generally also are bound to it by either the rule of their order, monastery, or their Abbot/Abbess.
While the specific content of each hourly prayer is subject to the hierarchy of the particular church in question, they are all prayers involving psalms, daily propers (Byzantine Troparia and Kontakia, and Irmosi).
It is advised that those seeking deeper understanding of their faith begin with simplified forms (which many bishops approve of) or common liturgical forms with others; those preparing for monastic or ordained life should be praying them anyway.
The hours are not required to be lead by a cleric, either, but certain parts are omitted when read by a “reader”, and certain others change form when lead by a deacon.
The Ruthenian pewbook has a simplified form of the office of Matins called “Divine Praises” preceeding the Divine Liturgy in the book. It lacks the references for the propers, but is a simplified version approved for all the Ruthenians in the Pittsburgh Metropolia.
Orthodoxwiki has a good discussion on the Byzantine forms (and terms for specific hours).
orthodoxwiki.org/Hours Byzantine Catholics are substantially the same, differing in minor ways from years of separation.