It's a magnetic coil gun. Yes, both use magnetism to accelerate a projectile; they nonetheless work quite differently, and conflating them is a bit akin to calling a cannon a rocket launcher. (Hey, those both use the awesome power of applied chemistry to accelerate a projectile...must be the same kind of weapon, then. :D)
Point taken... and that point, it is kinda the same problem that the real life gyrojet pistol has... it is a gun, it is a rocket... it's both. In the case of the Coil and rail gun, the difference seems to be more akin to smoothbored and rifled gun...
So you're saying that you want a quantam leap of weapons technology for a society that has just finished reviving Primitive equipment. This weapon is also based off of a weapon that functions on one principle but named after weapons that operate on a (somewhat) different principle. And this weapon isn't allowed to use any feature after the weapon it is named on, but has to be different from the system that it is based off of.
I'm not sure what it is that you actually want.
You have a point there. Then again, the setting seemed to have a group who just rediscovered a technology ('40) suddenly come out with the Light Gauss Rifle within 19 years of it's rediscovery. The Silver Bullet within 10. Heavy was 21 years. Clanners lagged behind a bit before introducing a next gen Gauss at 19 ('49) years after first contact with a dynamic people with the HAG and 20 years for the AP Gauss.
Now, making the assumption that there is a fun extra 15 years or so tossed on for the jihad... I kinda wrote my tiny short from the POV of 85 or maybe even 86, far outside the purview of what might fall within the universes' Jane's Fighting (fill the blank) for that year (AKA, the TROs). Now, building this POV for the work... assumed some lab jockey toyed around with some things. After all, mistakes and unexpected results are some of the most revolutionary things. Or perhaps the boy was sitting on a grav train one day not playing Angry Birds 3085 edition on his data slate and actually came up with an idea.
After all, except for force fields and anti-grav, we got pretty much everything else in Sci-fi laying around... complete with hand held lasers that actually can hurt someone... meaning we solved the battery problem we have today!
Bam, built a pseudo prototype using a half junked gauss rifle that was laying around (mythbusters style or how half the R&D departments I know operate), probably blew up half the lab in the first firing. Kept toying around with it. It is the closing days of the crusade to beat down the Jihad or just right after, R&D budgets are probably being slashed at this point or proposals for new weapons being pushed to the side in favor of mass production (or as close as we can get to it) to support the drive to Terra. This guy's team probably slap dashed the first series of prototypes using stuff they borrowed from around the factories or custom built it. Bingo, it worked. It probably has a terribly more complex name on the folder when they submit it up to the higher ups in the company.
They look at it funny. Who wants a H-JAV? That sounds terrible. We can't sell that! It would be as silly as calling it a HAG! Explain it to me. Insert sound of snoring as the lab boys explain all the higher up particulars of how the new weapon operates. All that sinks in is the fact that it weighs as much as a gauss rifle but its better... oh, and the extra set of rails needed to support the greater output. Genius moment from the higher ups, Rail gun! Pass it to marketing, marketing talks to the lab boys, they face palm as the H-JAV is now called a Rail Gun, they get the presentation Okay-ed by the higher ups, insert story from my initial post.
This moment in Dilbert-esque history has been brought to you by Lorina Sparkling Lemonade.
Now, got a better name for a next generation improved magnetically propelled projectile thrower that isn't a terrifying acronym? I am all ears.