Maybe it had something to do with case capacity. Magnum cases generally have larger capacities than non-magnums...just like a magnum of wine. Some of the old British big-bores used to be black powder, and then went to smokeless. I believe those ones were created the name "Nitro Express". There are some anomolies, like the .416 Rigby, .404 Jeffery, .425 Westly-Richards and so on. These were also early developments, in some cases earlier than the .375 H&H Magnum. So maybe Holland and Holland wanted to indicate that their case had a larger capacity, which has the benefit of lower pressure or higher velocity than a standard case. Then along came all of the "short" magnums like the .458 Win Mag, .270 Wby Mag, .338 Win Mag and so forth. These cases had larger case capacity than those rounds based on the 8x57 case or .30-06 case. In addition, they were based on a magnum, so the name probably indicated both: larger case capacity and based on magnum.
The new short magnums are similar in case capacity to the "old" short magnums, but they are related to the .404 Jeffery, which does not have the word magnum in its name. But by this time, many people equated the word magnum with higher performance, so to indicate "high" performance, the marketers may have decided to use the word magnum. Short may be indicating that the capacity is similar, but in a short package.
The Remington Ultra Magnums have more capacity, hence they are ultra.
End of virtually pointless dribble...