A clarification on terminology
You will hear different names for the Mass but they each mean slightly different things: Mass, Eucharist, Holy Communion.
When it’s being thought of as a sacrament, one of the seven sacraments of the Church, we refer to it as the Eucharist, or the Sacrament of the Eucharist.
When it’s being thought of as the gathering of priest and people, eg in church on a Sunday with all the prayers and readings, it’s usually referred to as the Mass.
Holy Communion refers to that moment towards the end of the Mass when priest and people receive the Body and Blood of Christ. By derivation the term “Holy Communion” has come to be used almost universally to refer also to the Body and Blood of Christ itself.
So, we come to Mass to celebrate the Eucharist in which we receive the Body and Blood of Christ in Holy Communion (or you could say “to receive Holy Communion”).
Other terminology associated with the Sacrament of the Eucharist
The Body and Blood of Christ which we receive in Holy Communion is referred to by Catholics as The Blessed Sacrament, particularly when it is referred to in the context of Eucharistic Adoration, a Catholic devotion in which we spend time adoring Christ in his sacramental presence in the Blessed Sacrament. The Blessed Sacrament is also referred to sometimes as “The Eucharist” by derivation.