TerrainData - Difference between alphamapResolution and alphamapWidth

In order to procedurally generate terrain, we need to be able to programmatically assign textures/splatmaps to it. Interestingly, searching for help on this topic yields some old code by a few different people, but surprisingly little explanation.

Right now, I am trying to better understand the corresponding TerrainData members. Particularly, what is the relation between alphamapResolution and the pair of alphamapWidth and alphamapHeight?

It appears that only alphamapResolution can be set and alphamapWidth and alphamapHeight both mirror that value. Is there any more to it? Does that mean that terrains must always be square for this to work?