I could be wrong but those two ideas sound the same, just that the partition postulate is more general. There is also the angle addition postulate.
The segment addition postulate states that if three points A, B, and C are collinear such that B lies between A and C, then the sum of the lengths of segment AB and segment BC is equal to the length of the entire segment AC.
Partition postulate states that the whole is equal to the sum of its parts
For context, I learned the partition postulate and not the segment addition postulate