Ive seen loading tips like "assault rifles with a Vladof barrel fire faster as you keep the trigger held"; this clearly refer to the "Spinigun" triple gatling barrel assault rifles. Aside from that and the Elemental accessory (which I believe is exclusively made by Maliwan) I don't really know how to recognize which parts come from other manufacturers. Note that these parts show up on other manufacturer's guns, I've seen Bandit and Jakob's Spiniguns and elemental guns from everyone but Jakob's.
Are there other parts that are made by specific manufacturers that show up on guns? Most parts appear to be exclusive to a manufacturer's guns (e.g. Tediore's clean, mass-produced aesthetic), but it's implied certain parts can be on other manufacturer's guns, like the Vladof rifle barrel. How can I recognize them?
You can check the manufacturers' parts directly using Gibbed's Borderlands 2 Save Editor (link is to the most recent version as of now, it's actively updated and I don't think there's a single page to always get the latest version).
Basically you just load up your character's save file, go to "bank" or "backpack" and you can check out your stored/current gear and what stats they have. You can also of course edit them, but that's not required (and make sure to save your game before doing any editing yada yada yada).
Different parts have different manufacturer options so there's really no easy way to tell what's what without looking through this tool (or recognizing the parts after becoming familiar with them via this tool).
If you're not sure how to use the editor, guides for the current version can usually be found in the Se7enSins forums for Borderlands 2 Modding. A stickied thread on there right now has a compilation of various related threads.
Vladof guns (and therefore also Vladof barrels) have the highest firerates. Tediore always have the explosive reload. Bandit guns (the ones with the horrible spelling) have the largest magazines. Maliwan guns are always elemental (and in general very good). Jakobs guns are old-style high damage (the revolvers that fire as fast as you can pull the trigger). Hyperion guns are more accurate the longer the trigger is held. Dahl guns aways fire in bursts when aiming down sights. Torgue guns always deal explosive damage.
Additional info: Guns name prefixes (such as "Perma-Sharp SMG") are dependent on certain gun accessorys. These are effects/modifiers like 50% more melee damage. Here is a complete list: Strength Gamer Guide: 'Borderlands 2' Accessory Prefixes List
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