The different EDI standards are pretty explicit about the sequence of messages (276/277, etc.), acknowledgments (technical, functional, etc.), and conversation items (interchange IDs, duplicates, sender/receiver IDs, etc.). And yes, there is a requirement that EDI transactions do something or represent something that does something, in a specific way.

EDI does a lot of things, but its transport and semantics are visibly decoupled, whereas in web APIs, they appear to be somewhat uniform.

Web API is far from vague; on the contrary, it might even be more stringent (and selective) as the inbound data goes via multiple stages of validation as opposed to EDI, which does "take-all" data, then either "parse all" or "reject-all".