Google Web History is an automatically turned on service for Google account users who use Google search while being logged into that account.
According to Google, it contains information about the searches users do, and the pages that get clicked on. Users can access the web history online, and Google uses the information to personalize the search results. (If you are a Google user, and logged in while using the search engine, you may want to consider turning off the Web History feature to block the information from being recorded by Google).
The Google Chrome history on the other hand lists the pages that users have visited while using the Google Chrome web browser.
A recent Chrome patch indicates that Google plans to merge Google Web History and the Chrome history. This basically means that Chrome users will not only see the history of the web browser, but also the history of their web searches in Chrome. While those may be identical if Chrome is the only browser used, it may add information to the history if other web browsers or computers are used while logged in to the same Google account.
I can't really say if the patch has landed in the latest Chromium versions already, as I do not make use of Google's Web History feature. The core reason for this is that I dislike personalized search results and everything that goes along with it. While Google may still adjust the results according to my location, IP and maybe even a fingerprint of the computer, it appears nowhere near as complete as if I would be logged in all the time with the Web History feature enabled.
It is also not clear how this will be integrated into the browser. It is however likely that the searches and web history will simply be added to the history in the Chrome browser.
Users who do not want the data to be merged can either disable the Web History on the Google homepage, or log out of Google when they use the browser.