How is the expired domain renewal different from a normal renewal?

Expired domains are moved out of the registrar that you use and made public after it was not renewed on time.

As an analogy, think of it as restocking products in a store (expired domains), and reserving one in the storeroom at the back of the store for you (renewal of domains).

When a store restock products, those products are available to the public, it means that anyone can purchased them.

When you reserve an item, it stays in the back of the store until the time the customer decides to pick it up. While members of the public will know, they cannot purchase that item because you already paid for it, and reserved it.

Putting that analogy into perspective, once your expired domain is renewed, the registrar has to move it back to them, and then inform everyone else about it (a.k.a. the propagation process)