This one is weird.
First, the fusion beams for Feds and Rebels have different stats [BUG 1]. We’ll call them the Fed Fusion and the Rebel Fusion. I noticed this when switched from a Fed cruiser hull to a Rebel cruiser hull in the ship design screen. Before that, even, I noticed that the graphics for the weapons module kept their Federation look in the module inventory even though I was working on a different species cruiser [BUG 2]. This corrected itself when I moved to another block of modules, like engines, and then back to weapons.
I also noted that when I recreated Bug 2 above, in addition to retaining the Federation weapon picture, the fusion gun retained the Fed Fusion stats. Furthermore, when I loaded the Fed Fusion onto a Rebel hull, it remained a Fed Fusion turret [BUG 3?]. It gets a little weirder. I could now correct the graphic glitch (again by switching to another module group, and then back to the Rebel weapons), and at this point I could click on the Rebel Fusion gun in the module inventory and then click-n-compare it to the Fed Fusion version, which quite clearly demonstrated a different set of statistics.
I then saved this weirdo Rebel-Cruiser-con-Fed-Fusion. I restarted the game, loaded the cruiser, and the weird weapon stats remained [BUG 4? -ish?]. I’ll get back to you if I can confirm that the Rebel Fusion and Fed Fusion indeed confer different in-game effects.
I observed that there was a significant difference in reload speeds between the Fed Fusion and Rebel Fusion, both of which were mounted on the same ship, the glorious HMS WeaponErrorTest2. Which rocked the tutorial single handedly, by the way. I award her gallant crew no less than two gold star stickers for an adequate display of space gunnery.