Because they're not "from the same year". They're from the same "series".
The series year shows when a major change to the design was made. When there is a minor change, the year stays the same, but they add a letter. That's why the bill signed by Ivy Baker Priest and Robert B Anderson is Series 1957, and the one signed by Elizabeth Rudell Smith and C. Douglas Dillon is 1957A. When Smith left her job as Treasurer and was replaced by Kathryn O'Hay Granahan, they became Series 1957B.
Priest and Anderson were Eisenhower administration appointees, while Smith and Dillon are from the Kennedy adminstration.
While exact prodcution dates aren't available, Series 1957 notes were delivered to the US Treasury from September 1957 to March 1961. Series 1957A notes were delivered to the Treasury between January 1961 and February 1963.
The switch to Series 1957 happened for a couple of reasons--the inclusion of "In God We Trust" on the backs of the notes, plus a change from the old printing presses (which could print sheets of 18 notes) to new presses that could print a 32 subject sheet. But they didn't have enough of the new presses to do all the $1 bills, so the older presses continued to print the previous series (Series 1935). 1935F notes were printed at the same time, and have the same signatures as your 1957, 1935G notes have the same signatures as your 1957A, and 1935H notes have the same signatures as the 1957B notes.
You'll find higher denominations with the same situation for the same reason--there are Series 1950 notes with the same signatures as Series 1963 notes (and some of them have the same signatures as your two notes). All the transitions makes it quite confusing sometimes. In fact, the Granahan/Dillon signature combination appears on _six_ different series: Series 1935H and 1957B $1 silver certificates, Series 1963 Federal Reserve Notes, Series 1950D $5-$100 Federal Reserve Notes, Series 1953C United States Notes, and Series 1963 United States Notes.
The last of the old presses was taken out of service in 1968