The vibrating string length is often confused with the total length of a string or even the total length of the instrument. The vibrating string length of a string instrument is the distance from the inside edge of the top nut to the inside edge of the bridge. This is the precise area in which a string vibrates.
Most manufacturers refer to strings by the size of the instrument but Thomastik Infeld often refer to the vibrating string length and especially when purchasing their viola strings, this is a useful measurement to know. Here is a very useful video by Thomastik-Infeld: