How do I resize the google search bar?

Why does Google not maintain uniform caching of queries for the google Chrome browser and the search bar on the page?

• The address bar of Google chrome browser and the search bar on the google page both serve the same purpose of feeding in queries into the search engine. If you look at the cached queries in the search bar when you open the google page in the chrome browser there is a difference, Why doesn't google maintain uniformity cause the user stays the same?

• Answer:

  The Omnibox (address bar of Chrome browser) contains more than just Google search history: it also contains searches on other websites, URL that you have typed in directly, as well as description of websites you have visited for URL autocompletion. You can test it out yourself by typing chrome://omnibox/ into the address bar, and then typing in a search term you have used before.