It is important that the distinction between High and Low Mass are not applicable to the Mass of Paul VI (Novus Ordo). Before Paul codified the new order of Mass, High Mass was sung and was far more solemn. Low Mass was primarily spoken and involved less music. A High Mass generally involved a choir where a Low Mass could easily be done with organ only.
Solemn High Mass was when a Deacon and Sub-Deacon were present. Solemn High Pontifical Mass was a Solemn High Mass where a Bishop or Abbot was the celebrant.
In the Novus Ordo of Paul VI, the only real distinctions are practical. While there is no name difference, there are usually clear distinction between Masses on Ferial Days (generally using only two scripture readings) and Feasts and Solemnities (generally three scripture readings). Many parishes offer at least one of what could be considered a type of “Low Mass” on Sundays, usually with little or no music, often earlier in the morning. However, other than music, there are no real differences in the Sunday Liturgies. These types of Masses are generally discouraged, as many simply attend those Masses because they are the shortest.
I kind of digressed a bit into rankings of days, but to answer your question very simply, unless you are attending a Mass in the Extraordinary Usage (which I think everyone should do on occasion), the terms High and Low Mass do not pertain to you.
Adam