In my experience:
If a church signboard distinguishes between "Sung Eucharist" and "Holy Eucharist":
- The "Holy Eucharist" service is not the main service. Usually it's scheduled at 8:00 a.m., or even on the Saturday or Friday night before, to provide people with a quick, no-florid opportunity to get to a weekly Church service without to much "ado" about it. It's often a 1662-style service with NO music, neither hymns or canticles. Typically, all the shorter options provided by the rubrics will be chosen, and any omissions allowed by the rubrics will be omitted. You'll get the collect for purity, the collect of the day, the readings and the gospel, a short sermon, truncated prayers of the people comprising at minimum a prayer for the church, prayer of humble access and confession, the consecration and communion, and blessing. Back when I was in university, Father Molyneux could do it in 20 minutes, including sermon and pausing for an emphesema attack in the middle of the consecration.
- pre-liturgical-reform (that would be, before the mid 70's) Sung Eucharist always meant the 1662-style service. Besides the above elements, a hymn would be included for a processional in, the the Commandments would be chanted a capella by the choir to Anglican chant form, with chanted response by the congregation to each commandment; addition collects would be chanted or said, the Psalm would be chanted and a "gradual hymn" added before the gospel reading, the Credo would be chanted by the people with organ accompaniment, an offertory hymn would be added after the sermon, with a chanted doxology following the offertory procession, additional petitions would be included in the prayers of the people, the Sursum Corda would be chanted a capella (English plainsong this time, rather than Anglican chant) with responses chanted by the congregation and the benedictus chanted; Agnus Dei and other canticles would be chanted by the choir during the communion; the Lord's Prayer would be chanted, the priest would chant the prayer after communion and the people would chant Gloria in Excelsis; and after the Blessing a recessional hymn would be added. The most common chant forms used were James Merbeck's Anglican chant with his original English plainsong form for the sursum corda.
- Since liturgical reform, "Sung Eucharist" usually uses modern diatonic 'chant' forms (Louise Tadman's being the most popular, with Marty Haugman a favourite in certain circles) and usually more liturgical elements are said, with only a few being chanted: usually the Agnus Dei, Gloria (which is moved to the front of the service) and the Lord's Prayer. It's relatively rare nowadays to chant the Psalm and the Credo, and it's vanishingly rare to hear either English Plainsong or Anglican chant. Also in modern services, the gradual hymn is often replaced by a gospel acclamation.
- Of course, in the most contemporary services, the chant and traditional canticles are replaced by praise-and-worship songs, sometimes with the intent that they serve the same purpose and sometimes with more flexible sense of the role of music in the service; and the organ may be replaced by keyboard and guitar. Such a contemporary service would usually not be called "Sung Eucharist", but it is possible.