Graduation is a dated event, which is what makes jewelry a good fit — the piece carries the day with it. The trap is choosing something that only makes sense on that day.
Pick a piece for the life after: something for the first job, the first apartment, the ordinary weekdays ahead. It will be worn far longer than anything that reads as a trophy.
Should it say "Class of" or the year?
The year. "Class of" tends to stop being worn after the first summer; a year on its own is just a number she can keep for decades.
Is a graduation gift from a parent different from one from a friend?
In scale, yes. From a parent, this is often the first real piece she owns, so choose the one she will still want at thirty. From a friend, keep it light and personal — the note matters more than the metal.