Practically all English-language Bibles translate the Greek poterion as “cup”
rather than chalice, as current English attributes a technical meaning to this word which it did not have in the original. In a similar vein the word calicem
in Latin can refer to many drinking and cooking vessels and not just those reserved for liturgical use.
These memorial acclamations constitute a novelty within the Latin rite, and they were only introduced with the liturgical reform. With the removal of the acclamation “Christ has died ,” which was found only in the English missal, the remaining three are basically scriptural quotes.
The entire article of which this is only a part can be read at cup instead of chalice.