The multiplier type serves two purposes. The first as you note is for documentation. The second is that if for the same transition type, timestep, iteration, etc… you have two records with different transition multiplier types, the two will be multiplied against each other whereas if you had two identical records with the same transition multiplier type, only one of them could be used and your run will fail with a message that looks like this: [Failure] A duplicate transition multiplier value was detected: More information…
The transition multiplier types thus allow you to have different forcing multipliers applied to transition probabilities simultaneously. Note that the multiplier types can be edited under Project Definitions | Transitions | Transition Multiplier Type.