Shakespeare presents a range of positions related to slavery, freedom, hierarchy, and servitude. Prospero and Ariel have a relationship that seems close to indentured servitude: Prospero did Ariel a service (freeing Ariel from the witch's imprisonment), and so Ariel owes service. While there is a strict hierarchy (Prospero's definitely in charge, and Ariel seems servile at times) here is comparative respect there, and eventually, Ariel is freed, suggesting that slavery can end and that those who deserve freedom should be given it eventually.
With Caliban, though, things are different. Prospero calls Caliban a "dull thing" and his slave. Caliban accuses Prospero of stealing the island from him, and curiously, while Prospero calls Caliban a liar in general, he never does seem to explain his right to rule. It is as if his magic, combined with Caliban's bestial nature (he tries to rape Miranda, and gets drunk) seems to justify slavery.
Taken together, the two relationships suggest that different people deserve different degrees of freedom.