I'm just going to go on a tangent, while still being on topic? Also there will be minor book spoilers. If you plan on reading the Forerunner Trilogy; skip this post.
The similarities between Human and Forerunner weapons ( as far as both using hard projectiles instead of plasma) can be traced more than 150,000 years ago. Ancient Humans and Forerunner were both given life by the enigmatic Precursors that had reign over the Milky Way. Both were designed as bipedal and organic. While their cultures evolved and ultimately became much different, they still held similarities. e.g. Combat skins, starships, colonization, and so on. Their weapons also turned out to be similar. It seems that most organic tend to gravitate towards ballistic type weaponry. The Covenant's main armaments could be called an exception and I'll go on about that in a minute. 150,000 years ago Ancient Humans used ballistics like Hardlight---
New tangent approaching. something I just thought of while typing this... Ancient Humans had at some point learned how to reverse engineer Precursor tech after their(the Precursor's) "defeat" by the Forerunners. This could have resulted in the Hardlight technology for weapons. "But Eidolon, the Forerunners use Hardlight!" You may be thinking. And I'm getting to that. What I propose is that Ancient Humans came up with it first, and the Forerunners primarily used light/beam weapons at that time. Much like the beams that sentinels and Monitors use. However, if I remember correctly, after the Forerunners defeated the Ancient Humans they got rid of most, if not all, of their weaponry. And entered a short era of "peace" which left them dangerously unprepared for when the Flood returned. Having scraped their own weapons they could have turned to the Ancient Human Hardlight tech in a desperate move to defend themselves. That could be why the Hardlight guns resemble the Current Human's weapons so much. The connections being suppressor and Assault Rifle, scattershot and shotgun, Boltshot and Pistol, and so on. Those connections exist because both sets were created by Humans.
And now about the Covenant's weapons. The many plasma guns were the result of the attempts of reverse engineering Forerunner technology. However with their limited understanding of the Forerunners they could only reach the Plasma stage. You can see how the Hardlight weapons influenced the many Plasma weapons. The Plasma Pistol has a similar design to that of the Boltshot and even shares it's Charging ability. The Plasma Rifle and storm Rifle are much like the suppressor. The Beam Rifle and Binary Rifle are also very similar and share the fact that they can only be shot twice before having to reload or cool down, however the Beam Rifle's shots can be timed to avoid cool down. And while against the Humans these weapons work really well; they are only reverse engineered Forerunner tech and overall that makes them inferior.