In the Ordinary Form, the rigid distinctions do not exist. We do not have separate names for a spoken in-and-out weekday Mass and a two-hour chanted Christmas Mass with choir and incense. I suppose you can call the latter one a “Solemn Mass” if you want, but I would not generally expect to see it listed that way in a program.
Lest one come away with a mistaken impression, doing away with the rigidity of the distinctions has indeed had several good effects. It means, for example, that you can have a weekday Mass with no choir, but still sing, say, the Gloria, the Lord’s Prayer, and the Agnus Dei. Under the old system, it was all or nothing, so if you couldn’t round up a Gregorian schola capable of doing the Introit, Gradual, Alleluia, Offertory, and Communio, not to mention the Credo, then you couldn’t sing any part of the Mass. You also couldn’t have incense unless it was a Solemn High Mass with deacon and subdeacon, but these were so rare that eventually the Holy See gave in and granted an indult to use incense at the Missa Cantata – which is technically a form of Low Mass, but which more parishes could actually arrange for from time to time. Still, you couldn’t just pull out the incense whenever you wanted. If you parish had three Sunday Masses and only one was a Missa Cantata with the choir, then the parishioners at the other two would get no incense (no Asperges, either, for that matter, nor sung dialogues) even if it was Pentecost or something.
