Basically the browser it the program you use to access any internet sites you may wish to look at.
Internet Explorer, Chrome and Firefox are the three main browsers.
A search engine is a site that allows you to search for other sites on the internet that may be of interest.
So you run the search engine (site) in the browser.
When you open the shortcut that takes you to Google, at the top of the page you will see a bar with the site address in it and will read something like http://www.google.co.uk
Instead of typing BBC in to the Google and then clicking on the link Google gives you, you could type the BBC’s site address straight in to that address bar.
So you could type http://www.bbc.co.uk or http://www.singletrackworld.com (in fact you can pretty much drop the www. these days) in that address bar and hit return and you will be taken straight to that page.
Google != the Internet
Cheers
Danny B