"Butane Battery" is indeed a brand name for the cartridges which, until a couple of years ago, were sold directly by Bright Spark, hence the recommendation to use them with their stoves. They do differ from some cheaper cartridges on sale in that they do contain some propane rather than being pure butane. Propane evaporates more easily so it increases the pressure in the cartridge. Thus while it is often present in the dome shaped ones (which can withstand a higher pressure) it is probably only present in a relatively smaller proportion in the "Butane Battery" type cartridges and in other types is absent. It will increase the performance at low temperatures when butane is reluctant to evaporate. However that is probably only true for a new, or relatively new, cartridge since the propane will tend to evaporate quicker and get used up sooner during use than will the butane. A partially used cartridge is probably almost pure butane and will perform badly if it is cold.
I always buy the "Butane Battery" make, not so much for the propane, but because I've used an awful lot of them over the years in my boat heater and so far (offers prayer to the river gods) I've not had one leak, whereas I've heard of problems with some similar cartridges. Having to bail butane out of the cabin using a bucket is not a task I want to try!
Peter