The Google Maps Geolocation API is an HTTP endpoint that accepts user-supplied JSON data about nearby Wifi networks and cell towers and produces an estimate of the user's location.
The HTML5 navigator.geolocation
object supplies a browser API that does some set of operations and then produces an estimate of the user's location. From the W3C geolocation spec:
The API itself is agnostic of the underlying location information sources. Common sources of location information include Global Positioning System (GPS) and location inferred from network signals such as IP address, RFID, WiFi and Bluetooth MAC addresses, and GSM/CDMA cell IDs, as well as user input.
The navigator.geolocation
function may make use of any information available to the browser application, including any information from the device's GPS hardware, if it has any. Of course, it may also make use of any third-party Web APIs (including, possibly, the Google Maps Geolocation API) that can be reached. There is no specified required approach or inputs that must or must be used; the browser can do anything in its power to make a location estimate. It may do a better or worse job than Google's approach, depending on their particular implementations, or the browser may (as you suggest) actually directly use Google's API.
In short, Google's API is a way to ask, "Based on this cell and Wifi info, tell me where I am." The HTML5 API is a way to tell the browser, "You have access to the Internet and all the physical inputs available to my device; find out where I am, somehow."
I'm not surprised to learn that, if no GPS is present, the browser might outsource its geolocation work to a third-party service like Google. Browser vendors are generally interested in making browsers, not writing a robust service to solve the hard problem of transforming cell/Wifi data into location information. Furthermore, it requires a tremendous amount of geospatial data about the locations of various towers and Wifi SSIDs. It would bloat the browser to hold all the information locally, and any attempt for thevendor to host the information remotely would functionally be setting up a competitor to Google's already known-good service.