Are weapon upgrades permanent or just for that particular instance of a gun?

In Bioshock Infinite, you can only hold two weapons at once. If I upgrade say, my pistol and later drop my pistol for a shotgun, do I have to re-buy the weapon upgrade if I later pick up a different pistol?

If this is the case, then is there any way to tell which pistol lying on the floor is the one with the upgrade?

No, upgrades unlocked will not apply to any "instance" of that gun.

So yes, you can drop your pistol and pick a new one later and you will still have all the upgrades you unlocked.

Think of it like you're upgrading your skill with a particular firearm, rather than upgrading the firearm itself.

Any firearm you find and upgrade, upgrades all firearms of the same type. (I know that sounds physically flawed, but that's how it works).