Well, you know the actual difference, I assume. You’re talking about how they are used.
Haunt is most often used as a huge Bleed element in a Bleed and Stampede strat, like:
Curse of Doom->Haunt->Bring in Ikky->Black Claw->Flock->
Haunt does double damage through the Flock, and Curse of Doom hits double.
This dumps a HUGE amount of damage into one target. This is why it is so much used against “Boss” pets, big single targets.
UA, of course, empowers your other two pets. On its own, in the most vanilla case, it is not a good deal.
Suppose you have three pets, and all of them can expect to do 1500 damage before they die. So 4500 damage total.
If you UA your Valk on the first move, you lose all direct damage from your first pet, and add 25% to the other two. So 3000*1.25=3750 total. If you throw in the 600+25% for a CoD first, you are about even, so long as most of that that 600 is not wasted.
So you want to use UA when your other two pets are expected to do significantly more damage than usual - say with a glass cannon or with a type advantage. And since the benefit is spread over two pets, UA does not have to be dumped into just one target,
And as I type this, several counterexamples come to mind, where you would use Haunt and UA differently. But those are the most common and easiest reasons.