Lutherans, Catholics, Eastern Orthodox are all denominations of Christianity. The Lutherans believe in three key things: sola scriptura- the Bible alone is a source of faith, sola gratia- salvation comes through grace alone, and sola fides- Justification occurs through faith alone. The Catholic church believes both faith and tradition are a source of faith, salvation comes from God but human beings have to cooperate with God's grace, and Justification is received from faith in Christ and faithfully living out his call. The Eastern Orthodox believes that the Holy Spirit proceeds from just the Father where the Catholic church believes it proceeds from the Father and the Son. The Eastern Church also does baptism, eucharist, confirmation all at the same time.
Similarities: they all believe Jesus is the savior, they all do infant and adult baptisms, they all believe in the trinity.