a song of ice and fire - Horn of Winter = Dragonbinder?

Is there any definitive evidence that the Horn of Winter sought by Mance Rayder is not actually a Dragon horn or indeed Dragonbinder itself?

At first we are led to believe that Mance found the Horn of Winter north of the wall and brought it south with his army to break the Wall. The horn is captured when Stannis Baratheon's troops routed the army, and was made fuel for Mance's pyre. Then we discover that..

Mance was bluffing - the horn was a fake (and not killed in that event!)

At around the same time or soon after, Euron Greyjoy turns up at the Kingsmoot with the dragon horn called Dragonbinder, claiming it came from Valyria. He gives it to his brother Victarion when sending him to 'fetch' Daenerys Targaryen (I can imagine how poorly that will go!).

This horn supposedly binds or controls dragons, but almost anyone that blows it suffers death from 'blackened lung' (though presumably Daenerys herself could blow it safely, given she has dragon's blood in her veins).

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Although the Horn of Winter was supposedly somewhere north of the Wall, and Dragonbinder was sourced from Valyria, some of the answers to What was Euron "Crow's Eye" Greyjoy doing in Valyria? display skepticism that Euron was ever in Valyria (so he might have actually obtained it north of the wall).

There are also some tentative links between dragons and 'things north' in that:

• Dragons can make dragon glass which is capable of killing White Walkers


• If dragons can make short work of Harrenhal, they can also make .. a breach in a wall made of ice! It is noted in the this answer on Dragons that..

Dragons are believed to be intrinsically tied to magic and the seasons of the world. Since dragons became extinct from Westeros, the power of magic dwindled and winters grew colder.

Which in turn suggests that if Dragons were brought to the Wall and destroyed it, the problem of the others would also abate, since the others are known to be associated with the cold/winter, if not only moving around in it, then perhaps even causing it.

Of course none of these tidbits are definitive evidence that the two horns are one and the same, so my question boils down to: Is there some evidence I missed that definitively rules out that the two horns are actually a single horn with two names?

Answer

I'd say not; but could be.

The whole thing with the magical horns in A Song of Ice and Fire seems to be kept quite vague - and it seems to be intentionally done by the author, George R. R. Martin. But they have been mentioned enough times to drive speculation, both in-universe and out-of-universe.

Known variants:

• Horn of Winter (Horn of Joramun)
  
  
  
  • Apparently Joramun "woke giants from the earth" when he blew it
  
  
  • Currently people believe that it will "bring down The Wall"
  
  
  
  
  


• Dragon Horn
  
  
  
  • A horn which can apparently control dragons
  
  
  • People believe that this is how the Targaryens / other Valyrians controlled their dragons; but there is no proof at this stage
  
  
  • Dragonbinder (Euron's horn) is apparently one such horn
  
  
  
  


• Kraken Horn
  
  
  
  
  • It is believed that there is a horn amongst the treasure of House Celtigar in Claw Isle which can "summon Krakens from the deep"^[1]
  
  
  
  

What we know for sure:

• Euron
  
  
  
  • Has found a very immaculately decorated horn which has Valyrian markings on it
  
  
  
  • It also lights up prettily when you blow on it
  
  
  • Ends up killing the user
  
  
  • This is speculated to be the Dragonbinder
  
  
  • We are yet to see it bind a dragon
  
  
  • Apparently found in Valyria itself
  
  
  
  


• Mance
  
  
  
  • Also has found an immaculately decorated horn which has markings of the First Men on it
  
  
  
  • Claims it is the Horn of Jorumun
  
  
  • Later revealed to be a fake (as OP pointed out)
  
  
  • Apparently found at the Frostfangs (North of the Wall)
  
  
  • No mention of any 'special' properties
  
  
  
  


• Sam The Slayer
  
  
  
  • Is in possession of a quite simple looking horn
  
  
  • Hasn't been used yet
  
  
  
  • Found at the Fist of the First Men in the same cache which Jon Snow and Ghost found the Dragonglass daggers and arrowheads
  
  
  • Left there by some unknown brother of the Night's Watch
  
  
  • There is speculation online that Sam actually has the real Horn of Winter^[2]
  
  
  • It would definitely fit the 'surprise' factor of: "Hey, remember that little worthless horn you found? Well, it happens to be the most important plot-device of The North"
  
  
  
  

There are also other rumours which believe that Sam's Horn of Winter is actually Dragonbinder, and Euron's horn is actually nothing (or the real Horn of Winter). We're yet to find out whether this is true and which horn they actually are; see here:

And finally, as GRRM has said in a recent interview; just wait and see:

[Interviewer] I think the broken horn that Ghost found with all the obsidian is the real horn of winter. It hasn't been mentioned yet though. Any comments?
[GRRM] Nope. Keep reading.