Atwood's "Hag-Seed", being a reinterpretation of Shakespeare's "The Tempest" means that there are a number of similarities (resonances) and differences (dissonances) between the two texts. This invites you to reflect on the aspects that Atwood and Shakespeare agree on and disagree on. For instance, a notable difference between the two texts is the setting. While the original play largely takes place on Sycorax’s island, Atwood takes the readers to present-day Canada, primarily at the fictional Fletcher Correctional Centre. This allows Atwood to establish a physical manifestation of the "prisons" where the characters of Shakespeare's play are metaphorically trapped. Therefore, despite the fact that Atwood's novel partially pays tribute to Shakespeare's play, she also needs to appeal to her immediate audience through her own writing and ideas.
On the other hand, a number of main themes of the text remain unchanged, despite having been appropriated for the purposes of the novel. The power of magic remains thoroughly explored with respect to the theatrical form. Additionally, showcasing the complexities of alienated figures, whether in literature or in real life appears to be an issue that concerns both authors. For instance, consider the suggestion that Atwood is telling Shakespeare and her readers that, in this textual conversation, there are some aspects of humanity that never change, regardless of the passing of time or the differing settings.
I hope this helps!