In Act III, scene 1, Ferdinand though a royal, serves as a willing slave to Prospero. He does this because he is in love with Miranda, saying:

The very instant that I saw you did

My heart fly to your service; there resides,

To make me slave to it

He performs Caliban's work of carrying logs, but does it without complaining, because of Miranda. When she offers to help him, he won't hear of it.

But if Ferdinand is a willing slave for Miranda's sake, she also promises to be his: "I’ll be your servant / Whether you will or no."

In the next scene, the action turns to Caliban, who, after drinking with Trinculo, and Stephano, claims to that he has been cruelly enslaved by Prospero against his will, "subject to a tyrant." He says the island is his, and, in fact, expresses the closeness he feels to the place that his been his home his entire life. From a post-colonial perspective, we can feel some sympathy for Caliban because of the way Prospero has treated him.

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.