You seem to have misunderstood Twinned Spell slightly.
It doesn't cause a second instance of the spell to target another viable creature within range; it causes the same instance of the spell to target two viable creatures within range instead of just one. The relevant section of Twinned Spell reads as follows (emphasis mine):
... you can spend a number of sorcery points equal to the spell's level to target a second creature in range with the same spell.
This has a couple of implications.
First off, for spells like Polymorph, both of the creatures you're targeting turn into the same creature. However, you can keep concentration on both creatures, as it is only one instance of the spell, as opposed to two.
Secondly, for spells with a damage roll (like Chromatic Orb), you roll the attack roll separately for each creature, but you only roll damage once.
For spells that require concentration, both creatures are affected by the concentration effect. For example, if you cast Twinned Witch Bolt, if you hit both targets, you deal 1d12 lightning damage to them on the first turn, and you can use your action to deal 1d12 additional damage on each of your turns to each of the targets. If you fail a concentration check, you lose concentration on the spell for both creatures, not just one of them. Whether moving outside the range of Witch Bolt ends the spell for one or both creatures is up for interpretation by your DM (a strict reading of the RAW would suggest it ends for both of them, but I would personally rule that it only ends for the creature moving out of range).
In short, your polymorph spell turns the two targets into the same kind of creature.