I think you’ve basically got the gist of this.
Once upon a time there was the REST API (for “most” operations); a separate REST-style API for Search (thus two “discrete” APIs); and Streaming.
Since 1.1 everything is basically marked as 1.1 and now we conceptually divide the API and docs between REST (including Search) and Streaming. There’s also the Ads API which is part of the 1.1 scheme of things, but requires whitelisting and intended for a narrower group of users and partners, so we don’t list it directly under the same section of docs as the “main” REST API.
Additionally these days there is also Gnip, which is a commercial offering.
We moved all of the documentation to a newer CMS last year around the time we launched Fabric at Flight (our annual developer event), and have been working since then to tidy up and consolidate a lot of the older docs. The FAQ and “what you need to know” docs certainly still need a lot of love to clarify. Really there shouldn’t be much need to call out the pre-1.1 differences at this stage as 1.1 has been the status quo for several years 
