Feast or Solemnity?

"Solemnities" are the days of greatest importance; then come "feasts" in the narrower sense; and then "memorials."
-Catechist

how do [these various designations] affect the celebration of a Mass?
The ranking of liturgical celebrations guarantees that the most important events in the Church's life will not be skipped. For example, if your parish church was dedicated on March 27, in most years the parish could have a special Mass on that date. But since Christians in the West will be observing that as the date of Easter this year, that solemnity outranks all other liturgical celebrations.

On solemnities, there are three readings, plus the Gloria and the Profession of Faith. On feasts, there are two readings, but only the Gloria. Memorials generally have two readings with no Gloria or Profession of Faith.
-St. Anthony Messenger