Welcome, Turtle!
I’ll start with a few of the easier differences.
There are 23 different Catholic Churches in union with each other. You are part of the Latin Church. Your Church’s patriarch is the Pope of Rome. There are 6 current patriarchs, each over a different one of the 23 Churches. Obviously, the other 5 patriarchs are eastern. The remaining 17 Churches have different hierarchal structures dependent on a lot of issues like their needs, politics, size, etc.
You are under the Latin Code of Canon Law. The other 22 Churches have the Eastern Code of Canon Law which means people in those Churches don’t have the same canons to follow as you. When they fast, rules about marriage, ordinations, feast days, all sorts of things are different. Each Church then also has its own particular law that adds on to the eastern canon law.
Your Church uses the Latin, Ambrosian, and Mozarabic rites. I never can get which of the religious orders’ rites are current, but they exist as well.
The Eastern and Oriental Churches use different rites. The most common is the Byzantine Rite. The eastern canon law defines a rite as “the liturgical, theological, spiritual and disciplinary patrimony, culture and circumstances of history of a distinct people, by which its own manner of living the faith is manifested in each Church sui iuris. The rites treated in this code, unless otherwise stated, are those which arise from the Alexandrian, Antiochene, Armenian, Chaldean and Constantinopolitan traditions.”
Some of the liturgical, theological, spiritual, disciplinary, cultural, and historical differences in the Byzantine rite include
- the disciplinary allowance of the ordination of married men
- the lack of Eucharistic adoration or Corpus Christ processions
- the Liturgies of St. Basil, St. John Chrysostom, St. James, and Pre-Sanctified Liturgy
- the Sign of the Cross made touching the right shoulder first with the fingers formed three together and two down
- a 1-year liturgical cycle
- a distinct calendar of saints, feasts, and fasts
- A requirement to be married in the Church by a priest because of a different theological understanding of who the minister of the sacrament is
- a use of icons in worship
- a lack of use of statues
- different traditional prayers and devotions
I’m sure this is enough to get things started.