What exactly is the differences between these two? To me, they both describe a
change and would translate to "has become" in English.

I haven't been able to find any sources of questions about this so I would
appreciate some help.
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question
grammar nuances
What is the difference between なっている vs なった。
なっている is continuous, so it means “has become” whereas なった is in the past
tense, so it means “became.” For example, 医者になっている (“I have become a doctor”)
versus 医者になった (“I became a doctor”). The nuance of these two is similar in
both Japanese and English. The first is continuous, implying that one is still
currently a doctor, while the second is more ambiguous; it could be that one
became a doctor and quit.
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answer
Lets start by breaking down なっている なる(dictionary form) → なって(てform) →
なっている(ているform)

The ている is used to describe **an action in progress** or a **past even
connected with the present**. So basically, なっている is describing something that
will become and that thing is either related to the past and is connected with
the present or the action of becoming is in progress.

My hair got longer. かみがながくなっています。

On the other hand, **なった is the past short form of なる.** So it means it became
and it is not describing an action that is related to the present or is
continuous. It's something that happened in the past.
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First of all, you should have a look at [this
answer](https://japanese.stackexchange.com/a/3140/7705) which does a very good
job explaining, among other things, the `ている` that you are asking about. As is
mentioned in the answer, whether or not `ている` takes on this meaning
representing a resulting state depends on the semantic content of the verb,
among other things. The rest of my answer obviously only applies to cases
where the resultative interpretation is appropriate. This is [usually
true](https://japanese.stackexchange.com/a/26224/7705) of `なっている`.

The difference between the resultative `なっている` to the past tense `なった` is a
lot like the difference between the English `have become` and `became`. On
paper, these both just mean that the some event of becoming happened some time
in the past - the difference is that the former places substantial emphasis on
the state resulting from that event being relevant right now.

For example:

> 警察官になったけど、最終的に先生になった
>
> I became a policeman, but ultimately became a teacher

Is fine with the right context; it sounds like these events happened in order
in the past.

> 警察官になっているけど、最終的に先生になった (???)
>
> I have become a policeman, but ultimately became a teacher (???)

This one doesn't sit well with me in either language. Of course someone could
be a policeman and a teacher at the same time, but `I ultimately became a
teacher` is weird here because it there's no clear ordering - it doesn't sound
like the speaker is done being a policeman.

**Edit:** You mention in some comments that `なった` is sometimes used in ways
that are most natural translate as `have become` in English. This is true, but
ultimately just boils down to what is acceptable usage of different verb forms
in Japanese.

> 彼は最近かっこよくなったね

Literally just means "you recently became cooler", although
[pragmatically](https://en.wikipedia.org/wiki/Pragmatics) this clearly means
something that we would express in English as "you've gotten cooler recently".
Ultimately this just comes down to the fact that there is not going to be a
perfect 1:1 correspondence between Japanese verb forms and English verb forms,
and that this structure happens to be more acceptable for this usage in
Japanese than in English.

The resultative `なっている` doesn't map 1:1 either - a lot of usages most are most
naturally expressed using the present tense copula in English.

> 窓が開いている (the window _is_ open)
>
> ガラスが割れている (the glass _is_ cracked)

And this distinction isn't perfect in English, either. If I ask about going to
a meeting and someone says

> The meeting ended an hour ago

They are obviously trying to make a point about the fact that the meeting is
_currently_ over, despite this being simple past tense. This point comes
across just fine whether or not you say something like `has already ended`.
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answer