Notes

Most of the weapon variants are very different. But the tooltips/stats aren't too clear about the differences. Best example I think is the BAR Telescopic vs the BAR Storm. The Telescopic stats say the accuracy is much, much better than that of the Storm. But this is only with the bipod deployed and the use of scope. So it's a completely different playstyle to get the best results.
A quick overview that might help:
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Shotgun
Factory - Better recoil recovery, less time between shots to stay accurate
Slug - Increased effective range, less spread makes you need to aim better at close range
Hunter - Sits between Factory and Slug
SMG
Factory - Better recoil recovery
Trench - Better hip fire
Storm - Less recoil
Rifles/snipers
Sniper - Highest magnification, bipod
Marksman - Less magnication, hold breath longer
Infantry - No scope, better recoil recovery
Carbine - Better accuracy while moving, better hip fire
LMG
Suppressive - bipod, larger magazine
Telescopic - bipod, smaller magazine, scope
Self-loading Rifles
Sweeper - Full automatic firing mode, better hip fire
Extended - Larger magazine, less damage per bullet
Sniper - Bipod, scope
Marksman - Scope

There are a view weapons where I too don't really see why you would pick one variant over the other, but for most guns there are definitely differences. Note that when a gun has a bipod, you need to use the bipod to reach the stats in the tooltip. There are also a few Experimental variants. These differ per gun. Read the gun description to see what they offer and pay specific attention to the firing modes