I attended an Eastern Orthodox liturgy a while back and I noticed that at the end, the congregation was allowed to take home the remaining Eurharist. Was this the Eucharist or was it just some other bread?
What the people received at the end of the liturgy is not the Eucharist. It is called “antidoran,” which is blessed bread given out after communion. In Eastern Orthodox Churches it is traditional to distribute the antidoran at the end of every liturgy. The antidoran comes from the same loaf as the consecrated Eucharist, but it is not consecrated but blessed. It hearkens back to the era in which Christians received communion infrequently, only once or twice a year. Because people didn’t receive communion, they would come up to receive the antidoran. Thus, antidoran literally means “instead of the gift.” Most Eastern Orthodox parishes will offer the antidoran to any baptized Christian, although some will only offer it to Orthodox Christians.
Do the Eastern Catholic Churches distribute blessed bread like they do in the Eastern Orthodox Churches?
The distribution of antidoran is common to both the Byzantine and Armenian liturgical traditions. I do not know if any other traditions use it. Among Byzantine Catholics, the practice varies. I know from personal experience that Byzantine Catholics of the Ruthenian Recension have largely abandoned the practice, although the antidoran is still distributed on certain feast days together with an anointing.