What's the difference between cloning and reindexing an index in Elasticsearch?

For example:

Clone API
Reindex API

When is each API best for what?

What does Reindexing mean in Elasticsearch?

Reindex is the concept of copying existing data from a source index to a destination index which can be inside the same or a different cluster. Elasticsearch has a dedicated endpoint _reindex for this purpose. A reindexing is mostly required for updating mapping or settings.

Why do we need to reindex?

REINDEX provides a way to reduce the space consumption of the index by writing a new version of the index without the dead pages. See Section 23.2 for more information. You have altered a storage parameter (such as fillfactor) for an index, and wish to ensure that the change has taken full effect.

You have the answer inside: "Reindex does not copy the settings from the source index. Mappings, shard counts, replicas, and so on must be configured ahead of time."