The technical terms are:
"Low Mass": Missa Privata or Missa Recitiva -- that is a "Private Mass" or a "Recited Mass"
"High Mass": Missa Cantata -- that is a "Sung Mass"
"Solemn Mass": Missa Solemnis
I prefer to use the terms: Recited Mass, Sung Mass and Solemn Mass. The " High/Low" difference is not always accurate, and there are plenty of variations on this.
At a Solemn Mass the Priest sings much of the Mass, with the Deacon and Sub-deacon assisting (particularly in singing the Gospel and Epistle). The Deacon assists the priest at the altar and sings the Ite Missa Est. The subdeacon helps set up the altar as well as singing the Epistle. The Faithful sing the Ordinary of the Mass. The choir (schola) sings the Propers.
At a Sung Mass the Priest sings the same parts of the Mass as at a Solemn Mass, but he also assumes the parts of the Deacon and Subdeacon, since these do not assist him. The Faithful and Choir do the same as at a Solemn Mass.
At a Recited Mass, the Priests recited all parts that he would have sung before. The Faithful may recite parts of the Mass they would have sung at a Sung or Solemn Mass. The choir may sing Latin or vernacular hymns as Processional, Recessional, at the Offertory and during Communion, but are not permitted to sing over the priest while he is reciting the Mass.