The usual nomenclature is that regular callbacks and async API calls are made and registered in the same process space as the caller. (E.g. passing a function pointer in C, or using “await” in modern languages.)

Webhooks are callbacks received over HTTP from a public API. They may not be programmatically registered at all, e.g. the callback URL may be configured manually in an admin dashboard. So the application has less control over webhooks vs. regular callbacks or async functions.

Not sure of the evolution, but maybe because 'callbacks' exist everywhere, but 'webhooks' are specific to REST APIs.