What are the differences between weapons of the same type in Fortnite Battle Royale?

Generally, Advanced versions of weapons (SCAR, suppressed Pistol, Tactical SMG, and Heavy Shotgun) are better stats wise, but its totally personal preference as to which one you use

Shotguns

Tactical shotguns shoot faster and do less damage than pump shotguns, and hold 8 shells as opposed to 5.

The Pump also takes a full second to pull out, while the tactical takes the standard half second.

The Heavy shotgun does damage comparable to the tactical, but allows for more range, which is both an advantage and a disadvantage, depending on the situation.

SMGs

Tactical smgs hold 5 more shots than suppressed SMGs, and do more damage, but are louder, making it easier to be found while shooting.

Pistols

The only difference between suppressed and normal pistols is damage and rarity.

Assault Rifles

The same as Pistols - damage and rarity are the only differences between SCAR and AR.