How does Aristotle's theory of the four causes, as laid out in Metaphysics, differ from Plato's causality theories as laid out in Timaeus?

In Metaphysics, Aristotle lays out
his four causes as answers to "why" questions. In other words, if we were to ask why
something is as it is, we would want to answer it with respect to the following four
reasons:
1) The corporeal, or material
reason/cause that something exists. This means: what is something made
of. Aristotle gives an example of a bronze statue. The bronze is what the statue is made
up of, and is the material cause for why the statue is as it is.
2)
The shape, form, or formal reason/cause of why something is
as it is. In the case of the bronze statue, its form, or its shape, is the formal reason
for why the statue is as it is.
3) The functional, or efficient,
reason/cause. This cause states that the reason why the statue takes the
form that it does is because it underwent an entire process of having its bronze melted
and poured into the mold of a statue. For Aristotle, it is not just that the artist made
it that explains how the statue came to be, rather the artist knew how to make it and
this knowledge is the ultimate functional, or efficient, cause of the
statue.
4) The ultimate, or final, reason/cause
that something is. Aristotle refers to this as "the end," which is "that for the sake of
which a thing is done." In other words, we are now considering reasons; we are
considering the reason why the statue exists or is as it is. One
possible answer is that the bronze artisan wanted to create it that way. Another is that
someone else wanted it that way. But for some things, Aristotle acknowledges that the
final cause is an unanswerable mystery.

These four principles of
causality are different from the ideas of being/becoming, or causality, that Plato sets
out in his dialogue Timeaus. The biggest difference is that Plato
is not as concerned with the process of causality as Aristotle is. In
Timeaus, it satisfies him simply to state that anything that comes
into being has a cause (28a4–6, c2–3). He also states that there are some things that
exist, such as thoughts, ideas, or ideal forms, that will always exist, but never
necessarily come into being (27d6). He further states that the universe is a visible,
tangible thing that has come into being (28b7; from 5a–c, and
4).

Hence, while Aristotle uses cause to explain "why" questions,
Plato uses being/becoming to explain the "why" questions without considering steps or
processes.