Q:

Why do some spells have a duration of 1 year, and others have a duration of a year and a day?

The spell Geas, in a level 8 slot, has a duration of one year. The spell Mass Suggestion, in a level 9 slot, has a duration of a year and a day.
I'm already familiar with the historical roots of the "year and a day" timeframe, but I'm curious about why some spells have that duration and others just have a 1 year duration.
Is there any statement from the designers about why this discrepancy exists? Speculation is not an acceptable answer.

A:

Legacy from previous editions and roots on fairy tales
A Year and a Day is a common trope on fairy tales and stories about witches. 

The time span of a year and a day has many situations — legal and magical — where it is significant. For one thing, it sounds impressive, being more sonorous than merely a year. For another, it's been used in Real Life. For a third, it makes it clear that the time is precise; "a year" is sometimes used to mean approximately a year, but a year and a day makes it clear that the exact time is indicated.

A lunar year (13 lunar months of 28 days) plus a day is a solar year (365 days).  Also, 366 days would be a full year even if a leap day was included.
It is also a term adopted by common laws for this exact reason.
Why some spells have a duration of a year?
Geas spell description should also have said "a year and a day" if they were written by the same designer who wrote Mass Suggestion. Or maybe it was simply a memory lapse of the designer.
We simply have a small problem of lack of consistency. 
This is the kind of issues that editors should look up for and fix. In previous editions, we have seen spells being referenced as having "24 hours" durations aswell as "1 day" durations. 5th edition did a much better job at fixing those inconsistencies, but some of them (like the one you found) are still here and there. They should be reported so they can be fixed on future printings of the book.
For instance, this same issue does not happen with the spell Planar Binding:

At Higher Levels: When you cast this spell using a spell slot of a higher level, the Duration increases to 10 days with a 6th-level slot, to 30 days with a 7th-level slot, to 180 days with an 8th-level slot, and to a year and a day with a 9th-level spell slot.

For all purposes, "a year" and "a year and one day" should be the same.

