That’s pretty much it. Memorials are the lowest class of days, feasts are next, and solemnities are the highest. There are different rubrics for celebrating the different classes of days, for example, at Mass on solemnities, we say the Gloria and the Creed and hear three readings from the Bible. On feasts, we say the Gloria, and hear two readings. Memorials receive two readings, and no Gloria.
There is a ranking: 1) solemnities, 2) Sundays, 3) feasts, 4) memorials, 5) optional memorials.
Interesting that you should use those 3 days as your examples:
Great information about the octaves. The octave is the seven days following the solemnity also including the solemnity. And there are just two of those octaves in the normal Latin calendar since the changes of Paul VI: Christmas and Easter. (I was an altar server during the time of the 1955 and 1962 Roman calendars.)
There are also Feasts of the Lord, which are a kind of semi-solemnity – When the date falls on a weekday it is celebrated like a Feast, but if it falls on a Sunday in Ordinary Time or of Christmas it is celebrated like a Solemnity.
Christmas is even kind of a minor octave. The days do not rank as solemnities and most are supplanted by other celebrations. The only day that naturally falls in the octave is 30-Dec, the 6th day, and even that gets bumped sometimes (Both last year and this year it is replaced by the Feast of the Holy Family).
Unless it was changed with the most recent revision of the Roman Missal, there are only 6 Solemnities with proper Vigil Masses on the calendar: Christmas, Easter, Pentecost, the Nativity of John the Baptist, the Solemnity of SS Peter and Paul, and the Assumption of the BVM. (Any other Solemnity or Sunday may anticipate the celebration the evening before with the Mass of the day).
