I use the green plastic cases. They fit exactly one box of Coghlan's storm matches (put in up and down), and are snug with both strickers (facing the plastic) on opposite sides of the case.
Does anyone know if there is a difference between the Coghlan's and the REI?
Yes, huge difference, literally. The REI have about double the combustible material compared to all others (see image below). The exposed wood ends do need to be trimmed down by about 1/8-3/16 inch to fit a conventional match safe. The REI are vastly superior to all others I have tested.
(Below: BCB = NATO Lifeboat, Safesport = most others)