To begin with we need to note the following distinctions in the "type" or degree of solemnity of the Mass being offered:
1. Low Mass (Missa Lecta)
2. Sung Mass (Missa Cantata)
3. Solemn Mass (Missa Solemnis -- sometimes also referred to as a 'High Mass" or "Solemn High Mass")
In addition to these basic subdivisions there is also the Pontifical Mass which has the following subdivsions:
4. Pontifical Low Mass
5. Solemn Pontifical Mass
Finally, there were traditionally also the variants on the Papal Mass which included the Papal Low Mass, the Missa Coram Summo Pontifice (Pontifical Mass in the presence of the Pope) and the Solemn Papal Mass. In essence these are simply extensions from the pontifical forms of the Mass noted above (nos. 4 and 5), and those pontifical forms are in turn merely extensions of the first forms, specifically numbers 1 and 3. To keep things simpler we will keep the Papal Mass out of the equation.
The common denominator in all of these forms is the chasuble. At a Low Mass, it is the only one of these main outer vestments you will see. (As people often learn better visually, let's break them down in this way.)
LOW MASS
Next we have the Sung Mass or Missa Cantata. A sung Mass is really a hybrid that sits half way between the Low Mass and the Solemn Mass. Essentially it is a Low Mass with incense and chant/polyphony; there is no deacon or subdeacon. In that regard one might well only see the chasuble, but it is the more common custom that the priest will also perform the rite of Asperges prior to the beginning of the Mass (where the faithful are sprinkled with holy water) and if so he wears a cope for this sprinkling rite. (I will transpose the vestments to show they are worn by the same individual -- i.e. the priest).
SUNG MASS / MISSA CANTATA
Next we have the Solemn Mass -- sometimes called a High Mass or Solemn High Mass in some places. The Solemn Mass builds further upon the vestments of the Missa Cantata, generally having the cope worn by the priest for the Asperges sprinkling rite, the chasuble for the priest of course, and then in addition the vestments worn by the deacon and subdeacon, namely the dalmatic and tunicle; the subdeacon also wears a large veil for part of the Mass (Offertory and Consecration) called the humeral veil.As we are now seeing the revival of these I would note that in the tradition of the Roman rite, the dalmatic and tunicle were traditionally dispensed with in penitential seasons and Vigil Masses, as well as on Good Friday. In such instances (excepting Septuagesimatide and the "rose Sundays") the dalmatic and tunicle were replaced by folded chasubles in Solemn Masses. The deacon would also exchange his folded chasuble for a "broad stole" within the liturgy. The other vestments remained the same.
PONTIFICAL LOW MASS
In the case of the Solemn Pontifical Mass however, this is quite another matter, particularly where the prelate is concerned. But in the first instance it should be noted that, here again, the Solemn Pontifical Mass simply builds upon the vestments that were found in the Solemn Mass. Namely, the chasuble, dalmatic and tunicle (or folded chasubles for penitential times). However, in addition to these vestments there is also an Assistant Priest who wears a cope, and there are also two Assistant Deacons who wear dalmatics (worn over their cassock and surplice instead of an alb).
In addition to this, the prelate himself not only wears the chasuble, he also wears the mitre, and beneath his chasuble he wears the pontifical dalmatic and tunicle (which are made of very light silk so as to make them more easily layered and breathable). In addition to this, the prelate also wears pontifical gloves, pontifical sandals and silk stockings called buskins (not shown in the illustration). There are additional four pontifical attendants who carry the mitre, crosier, book and bugia (a lit candle) who wear matching copes -- usually simpler in design from the main vestments.
SOLEMN PONTIFICAL MASS