How and why did Plato’s ideal polis differ from that of Aristotle?
The difficulty in answering this question has to do with Plato never speaking in propria persona and Aristotle often arguing from endoxa (the accepted opinions of the wise). There is really no scholarly consensus on what either of these two authors might have considered and ideal polis.
Aristotle is concerned with the moral development of the individual being affected by the state of the polis. He makes comments to the effect, for example, that in a well-ordered polis with good laws there would be no need for rhetoric, but just a simple statement of facts of the case. Education, poetry, and laws would all contribute to inculcating good moral habits in citizens.The two main works by Aristotle you should consult are Politics and Nicomachean Ethics, but Poetics and Rhetoric are also important.
Plato deals with the improvement of the polis at length in Laws, but this is not meant as an ideal city, but a slightly improved real city. In Republic, the city is described primarily as a mirror of the soul writ large, and thus may not be intended as a portrait of what a city should be, but just an extended metaphor.
The city, for Plato as well as Aristotle, is normally described not as an "ideal city" but as a city which provides the best environment for the ideal individual life, which is the contemplative or philosophic one. Both philosophers (and remember that Aristotle studied at the Platonic Academy for 20 years) have that shared goal, although Aristotle is more concerned with ethical habituation and Plato with transcendence.