Eucharist vs sacrament

Eucharist and sacrament both are nouns.

Word	Noun	Adjective	Verb	Adverb
Eucharist	Yes	No	No	No
sacrament	Yes	No	No	No

As nouns, sacrament is a hypernym of Eucharist; that is, sacrament is a word with a broader meaning than Eucharist:

Eucharist: a Christian sacrament commemorating the Last Supper by consecrating bread and wine
sacrament: a formal religious ceremony conferring a specific grace on those who receive it; the two Protestant ceremonies are baptism and the Lord's Supper; in the Roman Catholic Church and the Eastern Orthodox Church there are seven traditional rites accepted as instituted by Jesus: baptism and confirmation and Holy Eucharist and penance and holy orders and matrimony and extreme unction

Eucharist (noun)	sacrament (noun)
a Christian sacrament commemorating the Last Supper by consecrating bread and wine	a formal religious ceremony conferring a specific grace on those who receive it; the two Protestant ceremonies are baptism and the Lord's Supper; in the Roman Catholic Church and the Eastern Orthodox Church there are seven traditional rites accepted as instituted by Jesus: baptism and confirmation and Holy Eucharist and penance and holy orders and matrimony and extreme unction