Eastern Christianity refers collectively to Eastern Orthodoxy and Oriental Orthodoxy, especially when speaking more about what they share in common than about the ways they differ.
The term may also include Eastern-Rite Catholic churches, which are those branches of Roman Catholicism -- including only about 2% of Catholics -- that follow rules and customs similar to those of Eastern Orthodox churches; for example, their priests need not be celibate and their parish priests administer the sacrament of confirmation to newborn infants immediately after baptism via the rite of chrismation, and the infants are then allowed to receive communion. The Eastern Rite Catholics are subject to the eastern Catholic patriarchs, and thus indirectly subject to the Catholic Pope through the Catholic Patriarchs of the East.
Historically, Western Christianity developed in western Europe, whereas Eastern Christianity developed in Greece and the Near East. Today, however, the geographical distinction is not nearly as absolute.