Excellent responses in this thread thus far. I'll echo what others have noted: the reduced recoil loads achieve this effect either through less shot, less charge, or both. Having played with a lot of it side-by-side with standard buckshot loads in an 870, I definitely can feel a difference.
Along with less shoulder pounding and better control, it really shines for follow-up shots -- I find I can come back on target notably faster.
The two I've settled on are Remington's Managed Recoil line of 00 buck and slugs -- not only does the buck shoot easier, but it patterns better from my shotgun compared to anything else in the Remington line-up; and Federal's several Flight Control offerings -- as previously noted, their patterning is incredible at distance, and along with their eight and nine pellet 00 buck (I prefer eight) and slugs, their new 1 buck load has finally become widely available.
There is much discussion as to how much terminal velocity is traded-off for easier shooting in these loads; if anyone finds a definitive answer, I'd like to hear it -- I've seen good gel tests and lesser, reassuring anecdotes and concerning ones. In all my shooting and research, I'm satisfied that in any close-quarters encounter reduced recoil loads will work, devastatingly. On average, standard buck loads are considered effective to approximately 40 yards, with slugs to a little more than double that. I dial those in by about 25 percent for reduced recoil loads, which still leaves me plenty of room for likeliest needs. Your mileage may vary.
I'm all for getting your girlfriend on board for an ammo purchase by whatever rationale necessary

, but if I understand you correctly she has fibromyalgia; I don't think I'd encourage any 12 gauge use for her regardless of load -- with that condition, it's likely to be painful and off-putting no matter what. As CoMF noted, 20 gauge might be considered, but you have to choose your weapon and load with care: most 20 gauge shotguns are lighter than their 12 gauge counterparts, so even with the lighter 20 load, you end of with the same kick as a 12 because there's less weight to absorb the recoil; also, there's significantly less defensive ammo to choose from in 20 compared to 12. If you or she (or both) are truly intent on getting her into defensive shotgun use, I would not rule out .410 bore -- with some of the 00 and 000 buck defense loads in that caliber (designed for Governor-type handguns), out of a shotgun you're getting serious terminal velocity in a platform that kicks negligibly, as in .22LR rifle territory.