Something I’ve never gotten is that true neutral and unaligned seem to be the same in the long run. The only difference is that unaligned is for wild animals, and true neutral is for intelligent creatures - pne being driven by instinct and the other by choice.

Similarities

• Neither leans towards good or evil nor law vs. chaos


• Both do what seems right at the time

Differences

• The reasoning behind their action is the only one I can seem to find

Unaligned specifically describes the "alignment" of creatures that lack the intellectual capacity to understand morals and ethics, as the Basic Rules describes:

Most creatures that lack the capacity for rational thought do not have alignments—they are unaligned. Such a creature is incapable of making a moral or ethical choice and acts according to its bestial nature. Sharks are savage predators, for example, but they are not evil; they have no alignment.

What this is meant to convey is that a creature that lacks the capacity for moral reasoning can do things which would absolutely be considered evil (or good, or lawful or chaotic) actions, were it a creature with the capacity for moral reasoning, but that doesn't make it actually evil (or good, or chaotic or lawful).

To take an example from popular culture, the common domestic housecat has a reputation for apparent sadism and cruelty based on how it hunts and "plays with its food". Were the cat an intelligent creature who chose to act that way towards its prey, it could quite fairly be called evil; it effectively often tortures prey animals for no practical purpose. However, a cat is not capable of moral reasoning, and it is not reasonable to ascribe an alignment to it - the game makes this explicit by calling such creatures unaligned.

Being unaligned is not the same as being neutral, since being neutral describes an intelligent creature that takes an overall neutral moral/ethical stance, but an unaligned creature could display any manner of cruel, altruistic, random or ordered behaviour without that having any impact on its mechanical alignment.

The reasoning behind their actions is what alignment means

You hit the nail on the head when you said

unaligned is wild animals and true neutral being for intelligent creatures.

Alignment is a choice (most of the time), it's a philosophy and world outlook that a creature capable of thinking uses to interact with the world.

Animals (and certain other things like oozes, aberrations, monstrosities, whatever) lack the intelligence to choose to follow their alignment, they just do. A wolf or a cow or a black pudding doesn't choose to eat things, it just reacts based on instinct. They are amoral (lacking morality).

Carcer pointed out that outsiders like Fiends and Celestials also cannot choose their alignment, it's intrinsic to what they are, but they can still choose their behavior based on their alignment, whereas an unaligned thing doesn't choose at all.